In the first presidential debate Wednesday night, President Obama and Republican nominee Mitt Romney packed their responses with accusations about each other's policies and defenses of their own.

Here are a few claims that deserve a deeper look:

Private-sector job gains

Claim: Obama said the U.S. economy has created 5 million private-sector jobs the past 30 months.

Facts: After the economy plummeted in late 2007 and throughout 2009, the United States has gained 4.6 million private-sector jobs since the labor market bottomed in February 2010 - or 5.1 million under preliminary revisions released last week that are not part of the official tally by the Bureau of Labor Statistics.

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Still, that's weak by historical standards. Under President George W. Bush, the private sector also added 5 million jobs in the 30 months after employment hit bottom following the 2001 downturn, and the pace of private-sector gains in the previous two recoveries was far stronger.

Tax cuts

Claim: Obama says Romney's tax plan would cut taxes by $5 trillion over 10 years, inflating the deficit.

Facts: Romney has proposed cutting tax rates by 20% in each bracket, which, the liberal Center for Budget and Policy Priorities says would cost $4.9 trillion over 10 years. Romney said his plan will be paid for by curtailing tax deductions, so middle-class people pay less overall and upper-income people don't see lower taxes. Last month in Ohio, Romney said middle-class people would see little change in their taxes under his plan.

Romney has declined to say what tax deductions he would end. The non-partisan Tax Policy Center has contended that middle-class families would see taxes rise about $2,000 a year under Romney's plan if he keeps his promise to make the tax reform revenue-neutral, arguing that it can't be done without ending popular middle-class deductions on mortgage interest and charitable contributions.

The American Enterprise Institute, a conservative-leaning think tank, has said that the gap can be closed by ending tax breaks targeting the wealthy, including tax exemptions for interest on municipal bonds.

Romney said he would not raise taxes and would not approve any tax cut that would expand the deficit. He argued that tax cuts will increase investment, putting more people to work and increasing the taxpaying population. 

The middle class

Claim: Romney said middle-class families' income is down $4,300 since Obama took office.

Facts: According to a March 2012 analysis by Maryland-based economic consulting firm Sentier Research, Romney was correct. According to their analysis, based on February 2012 Current Population Data compiled by the U.S. Census, the median household income was $50,065 in February, compared to $54,481 in December 2007 - right before the recession started, and nearly 11 months before Obama was elected.

The current median household income is $50,678.

What Romney didn't say is that the decline in real median household income has been occurring over the course of the past decade, well before Obama took office. The trend has continued under the Obama administration, but it did not start there.

Taxes for the wealthy

Claim: Romney says he wouldn't cut taxes on the wealthy.

Facts: Romney wants to cut personal taxes by 20% for everyone, including the wealthy. He also wants to cut taxes on interest, dividends and capital gains for Americans with adjusted gross income below $200,000.

Obama, however, wants to return taxes to Clinton-era rates for individuals who make more than $200,000 in annual taxable income and families who make more than $250,000 in taxable income. So Romney wants to maintain tax cuts for the wealthy that Obama would eliminate.

Energy independence

Claim: North America can become energy independent under Romney's plan, creating 4 million jobs.

Facts: This is likely to happen anyway, possibly as soon as the end of the decade, Citigroup said in a book-length report earlier this year.

The key factor is not changes in policy, but changes in drilling technology that have let America increase oil production faster than any other nation in the world in the past four years, Citigroup said.

Declining crude oil imports, and more exports of natural gas and refined oil products, could reduce the trade deficit by as much as 40%, adding 1% a year to economic growth, Moody's Analytics estimates. Citgroup estimated that the emergence of the United States and Canada as a "new Middle East" could add 3.6 million jobs.

Medicare cuts

Claim: Romney said Obama's health care law cuts $716 billion from Medicare which will hurt current beneficiaries.

Facts: This has been one of Romney's favorite lines of attack, but his claim that Obama's health care law cuts $716 billion in benefits for current Medicare beneficiaries is not true. The health care law will limit payments to health care providers and insurers - not senior citizens' benefits - as part of an effort to rein in costs over the course of the next decade. Romney and other opponents of the law, however, contend that the payment cuts would affect seniors' benefits as an unintended consequence because they assert doctors will stop accepting Medicare patients and it could force some health care facilities to close.

The law has not yet been fully implemented, so the cuts' effects on beneficiaries are uncertain. But the law as written does not cut benefits for senior citizens. It is also worth noting that Romney's running mate, Rep. Paul Ryan, R-Wis., included the same spending cuts in his own 2012 budget blueprint that House Republicans supported with near unanimity.

Clean energy

Claim: Romney said clean energy interests got $90 billion in tax breaks under Obama, and that half of those companies receiving breaks went out of business.

Facts: The president's 2009 stimulus bill included a combination of over $90 billion in spending, financing and tax breaks for clean energy investments, but it's false that half of the companies went broke. Some of the Energy Department's loans went to firms that failed, most notably the solar energy company Solyndra, which cost taxpayers $535 million, but Romney's claim that half of the companies went broke is inaccurate. In a 2011 story, USA TODAY reported that the stocks of many of 45 publicly traded companies receiving stimulus funds had outperformed the stock market, despite Solyndra and other, smaller failures. The money, mostly in loans and loan guarantees, are helping build factories for companies such as Ford, Nissan and Tesla Motor. One beneficiary is health care technology company Athenahealth, whose shares have more than doubled. Its CEO, Jonathan Bush, is a first cousin of President George W. Bush.

Size of government

Claim: Romney said Spain spends 42% of its economy on government and the United States does, too.

Facts: Romney's claim appears to be based on the "Index of Economic Freedom," a compilation of economic statistics put together by the conservative Heritage Foundation in conjunction with the Wall Street Journal. Given that source, Romney's numbers are off, but in the ballpark.

According to the index, Spain spends 45.8% of its gross domestic product on government. That's before severe austerity measures were announced last week in a "crisis" budget that cuts government ministries by 9% across the board. The comparable figure for the United States, according to the index, is 42.2%. But it should be noted that federal spending accounts for only about 24% of the economy, according to the Office of Management and Budget. The remainder, which comes from state and local spending, roughly squares with estimates of government spending by the U.S. Census Bureau.

Rising health care costs

Claim: Health care costs have risen $2,500 per family per year under Obama.

Facts: Partly true, but health care inflation has slowed notably under Obama. Health insurance costs rose 4% last year, according to the Kaiser Family Foundation. That rate is far below the 10% to 13% seen in 2003 and 2004. Kaiser says the average employer-sponsored family health insurance policy costs $15,745, compared with $12,680 in 2008. The portion paid by workers, after employers' contributions, rose to $4,316 from $3,354.

"Rates of increase in total health spending have been holding at 4%-6% per year recently," Kaiser CEO Drew Altman wrote Sept. 12. "Per capita spending - which is most analogous to premiums - has been rising about a percentage point below that. These are strikingly low numbers to those of us who have been studying health costs for a long time. A 4% increase in health premiums is good news.''

Health care

Claim: Obama's health care law is "essentially the identical model" of Romney's Massachusetts health care law.

Facts: Romney's Massachusetts health care law served as the policy basis for Obama's health care law, and the two laws include many of the same foundations, such as coverage for pre-existing conditions. An NBC News analysis of White House records show that senior White House officials had at least a dozen meetings in 2009 with health care advisers who also helped shape Romney's 2006 law. Romney's law received significant bipartisan support from Democrats, unlike Obama's which was largely opposed by Republicans. "Like Obamacare, the Massachusetts law includes a mandate that individuals buy private health insurance, and offers subsidies to those who need them."

Tax hikes for the wealthy

Claim: Romney said raising the personal tax rates for the wealthy would kill jobs because many small businesses pay taxes as individuals.

Facts: About 3% of small businesses earn sufficient income to be impacted by higher individual taxes, though many of those are among the most successful who do a lot of hiring and investing, according to Moody's Analytics. Still, Moody's chief economist Mark Zandi says it's stretch to argue that raising the rate would significantly impact small business hiring.

Salesforce.com CEO Marc Benioff said Silicon Valley entrepreneurs rarely consider tax policy in deciding where to begin companies, saying it's "ridiculous" to assert that changes in capital gains taxes and top tax rates will have a meaningful impact of formation of high-growth start-ups.