(NBC NEWS) -- Senators formally announced a compromise amendment on border securityprovisions Thursday designed to woo GOP support for a comprehensiveimmigration reform bill, hours after lawmakers voted to set aside a morestringent border measure that Democrats had dubbed a "poison pill."

RepublicanSens. John Hoeven, N.D., and Bob Corker, Tenn., worked with Gang ofEight Sens. Chuck Schumer, Bob Menendez, John McCain and Lindsey Grahamto draft the "border surge" plan, which would double the size of theborder patrol, require 700 miles of border fencing, and require adetailed comprehensive south border security plan including high-techprotections.

"We have, if this legislation passes in the form thatit is, with the amendment as we've agreed, we have secured the border,"Corker said on the Senate floor.

Democrat Chuck Schumer, whohelped draft the original bill and worked on the border compromise, saidthe amendment "answered every criticism" of the legislation.

"It is safe to say: This agreement has the power to change minds in the Senate," he said.

Thelanguage of the amendment is currently being vetted, the senators said,and is likely to be introduced later today. Others signed on thelegislation include the Republicans in the Gang of Eight as well asRepublican Sens. Kelly Ayotte of New Hampshire and Dean Heller ofNevada.

Earlier Thursday, the Senate voted to table - oreffectively kill - the legislation by Republican Sen. John Cornyn ofTexas that would have instituted new border metrics and required thosegoals to be met before undocumented workers can apply for green cards.Democratic leaders called that amendment a "poison pill," and VicePresident Joe Biden told attendees at a Hispanic prayer breakfastThursday that the Cornyn measure was "one of the meanest amendments thatwill come up in the Senate."

Cornyn said on the Senate floor thathis amendment would provide promises of results rather than "falsepromises" about border security goals.

But supporters of the new compromise say that its provisions alsooffer assurances of "dramatically" beefed-up border security and wouldprevent future waves of illegal immigration.

"For people who areconcerned about security, once they see what is in this bill, it'salmost overkill," Corker said on MSNBC's "The Daily Rundown" Thursdaymorning.

Sen. Marco Rubio of Florida, a key Republican on the Gangof Eight who has been pushing for more border security additions to thelegislation he helped draft, backed the amendment in an interview onFOX News, calling it "a dramatic expansion and improvement in bordersecurity that I hope will allow finally for this legislation to have thesupport it needs."

The additional provisions will come with aprice tag. Aides estimate that the doubling of the border patrol agents-- just one piece of the "border surge" -- will add about $30 billion tothe overall cost of the bill, though the Congressional Budget Officehas offered no formal accounting of the measure yet.

Supporters ofthe legislation argued last week that increasing border patrol agentswould be unnecessarily costly. But after a Congressional Budget Officereport estimated that the flow of undocumented immigrants into thecountry would only be marginally decreased under the originallegislation - and without another workable alternative to buildconservative support for the bill - backers accepted the increase asnecessary and affordable because of the bill's other estimated positiveeffects on the economy.

"I can tell you this: It's money wellspent because it makes the border more security because it helps us withour sovereignty," said Sen. Lindsey Graham, R-S.C.

The compromisetalks were aimed at winning over enough Republican votes to pass acomprehensive immigration reform bill with an overwhelming majority ofsenators -- without angering Democrats who want to make sure that thepath to citizenship included for undocumented immigrants isn't affected.A strong margin of victory for the legislation in the Senate is seen asheightening pressure on the more conservative House of Representativesto adopt the landmark immigration law.

"We have some people in ourcaucus that are never going to vote for an immigration bill, OK, Idon't care if you -- it's just never going to happen," Corker toldreporters Wednesday. "And so we realize that. And yet there are peoplewho, with the right provisions, would."

There are signs that thestrategy is working. Sen. Mark Kirk, an Illinois Republican who votedagainst an initial measure to bring the bill to the Senate floor, saidThursday that he is now prepared to support the immigration bill if theborder security amendment is included.

"This bipartisan compromise will restore the people's trust in ourability to control the border and bring 525,000 people in Illinois outof the shadows.," Kirk said in a statement. "Once the Senate adopts ouramendment, I will be proud to vote for a bill that secures our borderand respects our heritage as an immigrant nation."

There's a smalluniverse of Republicans that have also given early indications thatthey'll support the bill -- the four Republicans in the Gang of 8; NewHamsphire Sen. Kelly Ayotte; and Sen. Lisa Murkowski of Alaska.Republicans including Corker, Sen. Lamar Alexander and Georgia Sens.Johnny Isakson and Saxby Chambliss have also been considered possiblesupporters.

But Senate leaders and the Gang of Eight negotiatorshave been hoping to draw half the Republican conference to support thecomprehensive legislation.

The most vigorous opponents of thecompromise bill maintain that the Hoeven-Corker measure still does notdo enough to prevent illegal immigration. The political arm of theHeritage Foundation, led by former Sen. Jim DeMint, says it opposes theamendment because it "fails to take a security-first approach," andimmigration limitation group NumbersUSA is urging its members to lobbyagainst the measure.

Speaking in opposition to the amendment,Sen. Ted Cruz of Texas called it a "fig leaf," and Sen. Jeff Sessionssaid it would merely "throw money at the border" without fixing theproblem of illegal immigration in the future.