Story Highlights• Compromise reached requires $4 billion for security, enforcement
• Comprehensive immigration bill had stalled last week in Senate
• Senators might be able to trade limited changes for holdout votes
• Measure could be reconsidered as early as end of next week
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WASHINGTON (CNN) -- Just a week after an immigration reform bill appeared to stall on the Senate floor, Senate leaders reached a bipartisan deal Thursday evening to bring it back for consideration as early as the end of next week.
Senate Majority Leader Harry Reid and Minority Leader Mitch McConnell issued a joint statement announcing debate on the measure will resume after the Senate finishes work on an energy bill expected to take up most of next week.
Details of the agreement have so far not been disclosed. However, senators and aides familiar with the deal said it will allow for consideration of about 20 amendments once debate resumes.
Reid pulled the bill from the floor last week after most Republicans balked at cutting off further amendments and moving toward a vote. The Democratic leader said he was willing to revive the bill if it was clear there was enough Republican support to move the bill forward.
A tentative agreement was reached after a full day of negotiations in an office near the Senate floor. Reid, McConnell and key architects of the bill then met to reach final agreement on the details.
Thursday's breakthrough came just hours after President Bush threw his support behind an amendment -- sponsored by Republican Sens. Jon Kyl of Arizona and Lindsey Graham of South Carolina -- that would provide an additional $4.4 billion for border security and work site immigration enforcement. The amendment is a bid to answer concerns from some GOP critics that the security aspects of the bill weren't tough enough.
"We're going to show the American people that the promises in this bill will be kept," Bush said.
In addition to beefing up border security and increasing the number of Border Patrol agents, the immigration measure would create a guest worker program, which would allow migrant workers from other countries to work temporarily in the Untied States.
The most controversial aspect of the bill is the creation of a pathway to legalization and eventual citizenship for the estimated 12 million illegal immigrants already in the country, an idea which critics dismiss as "amnesty."
But Bush, speaking Thursday to the Associated Builders and Contractors -- a group whose members rely on immigrant labor -- insisted once again that the bill's pathway to legalization is not amnesty.
"Amnesty is forgiveness with no penalty for people who have broken our laws to get here," he said. "This bill requires illegal workers to pay a fine to register with the government, to undergo background checks, to pay their back taxes, to hold down a steady job and to learn English in a set period of time."
Bush also said some opponents of the bill seem to "believe that we could just kick (illegal immigrants) out of the country."
"That's just totally impractical. It won't work," Bush said.
President Bush met with Republican senators on Tuesday to try to find votes for the immigration bill.