A Republican-led Senate committee last week defied Bush and approved terror-detainee legislation that Mr. Bush vowed to block. Sen. John Warner, normally a Bush supporter, pushed the measure through his Senate Armed Services Committee by a 15-9 vote.
White House Deputy Press Secretary Dana Perino said the administration was sending the revised language in hopes of reaching agreement.
"Our commitment to finding a resolution is strong," Perino said. "This legislation, once finished, will provide not only a way to bring the mastermind of 9/11 to justice, but also provide clarity to our men and women in the intelligence community who are interrogating these high-value detainees who helped provide information that allowed us to disrupt and prevent additional terrorist plots against America."
A top White House source tells CBS News White House correspondent Bill Plante "'we're trying out some new language,' but doesn't expect anything tonight."
"There's no deal yet, but one of the people who is familiar with all this says 'the doors are open again,' and he now believes there is a 50-50 chance they can reach an agreement, if not in the next few days, before Congress adjourns later this month," CBS News chief Washington correspondent Bob Schieffer reports.
Sources also tell Schieffer that the president wants an explicit assurance in the law that the CIA can continue to effectively interrogate prisoners.
An administration official, who declined to be identified because of the sensitivity surrounding the negotiations, said the new language only addresses a dispute over the nation's obligations under the Geneva Conventions, which sets the standard for treatment of prisoners taken during hostilities.
So, what are the tough tactics the CIA wants to use?
"Sleep deprivation, long periods of standing, other types of things that will try to wear down a detainee's resistance to questioning," former CIA official and CBS News consultant John Brennan tells CBS News national security correspondent David Martin.
Tom Malinowski of Human Rights Watch tells Martin that depending on how harshly the techniques are applied, they could violate the Geneva Conventions.
Malinowski says these include "forced standing, where the prisoner is forced to stand motionless for up to 40 hours at a time," and "induced hypothermia, in which a prisoner is subjected to extremely cold temperatures."
The House on Monday backed away from a floor vote as planned this week. No vote in the Senate has been scheduled.
The White House was adamant last week that the Senate proposal would end the CIA program to interrogate terrorists. Top officials spoke with reporters and senators in a bid to shore up support for Mr. Bush's legislation instead.
What triggered the compromise? Schieffer reports that both Sen. Lindsey Graham, R-S.C., and Steven Hadley, the White House national security adviser, appeared separately on CBS News' Face the Nation Sunday, but they talked for about 45 minutes outside the studio.
"It was an off-the-record conversation, but I think both of them would tell you that's what really got this started," Schieffer says.
Whether Mr. Bush would have enough votes to win on the Senate floor remained unclear. On Monday, Warner appeared to have the majority of support in the Senate, with at least 52 votes in their favor if Democrats backed them as expected.
GOP Sens. Chuck Hagel of Nebraska, Lincoln Chafee of Rhode Island and Olympia Snowe of Maine said they favor Warner's bill, joining Warner and three others who voted for it during the committee meeting last week.
There are 44 Democratic senators plus a Democratic-leaning independent, Sen. James Jeffords of Vermont.
The president's measure would go further than Warner's bill, allowing classified evidence to be withheld from defendants in terror trials and using coerced testimony. Mr. Bush also favors a narrower interpretation of the Geneva Conventions that would make it harder to prosecute U.S. interrogators for using harsh techniques than Warner and his allies support.
Several conservatives have lobbied on Mr. Bush's behalf in Congress, including leadership and Sens. John Cornyn of Texas and Jeff Sessions of Alabama.
Neither side has been able to muster definitively the 60 votes necessary to prevent a Senate filibuster of their proposal. This uncertainty, along with hope that the White House and Warner would reach an agreement to stave off a Republican showdown on the Senate floor has kept the bill from being voted on.
Senate Majority Leader Bill Frist, R-Tenn., who supports the president's bill, has said he wants to pass the bill before lawmakers recess at the end of the month. Doing so would allow the president to proceed with prosecutions of 14 "high-value" terrorists before the midterm elections.
The president's plan has encountered resistance in the House as well, with Rep. Steve Buyer, R-Ind., urging Bush to heed the military's top uniformed lawyers, who have previously opposed some provisions of the president's plan.
An agreement would keep Republicans from having to choose between backing Mr. Bush, as they have done in the past on anti-terror issues, and three Republicans known as leaders on national security issues: Warner, R-Va., a former Navy secretary; John McCain, R-Ariz., a former prisoner of war who last year pushed through legislation banning mistreatment of detainees; and Graham, a reserve judge for the Air Force Court of Criminal Appeals.