A House panel on Wednesday first rejected but then approved the Bush administration's plan for prosecuting and interrogating high-value terror suspects while top Senate Republicans met with President Bush at the White House over a compromise plan for handling the detainees.

The House Judiciary Committee first decided on a 20-17 vote to send the president's terror detainee bill to the House floor with an unfavorable recommendation, but later in the afternoon Republicans held a second vote and approved on a 20-19 tally to send the bill forward with a favorable recommendation.

Rep. Louie Gohmert, R-Texas, first cast an unfavorable vote, which allowed him to bring up a second vote under House rules. He cast a favorable vote the second time around. Two other Republicans — Illinois Rep. Henry Hyde and California Rep. Elton Gallegly — who were absent during the first vote joined Gohmert for the second chance.

Two Republicans — Arizona Rep. Jeff Flake and South Carolina Rep. Bob Inglis — joined all 17 committee Democrats voting unfavorably. Rep. Ric Keller, R-Fla., was absent because his wife just gave birth.

The panel's vote signals that most of its members present were comfortable with the president's plan to clarify elements of the Geneva Conventions on permissible activities for interrogating detainees.

Earlier in the day panel members voted 18-17 against an amendment by Reps. Adam Schiff, D-Calif., and Jeff Flake, R-Ariz., to bring that bill more in line with the Senate version of the provisions for CIA agents to question suspected terrorists. Inglis supported the amendment.

By voting favorably for the administration's plan and rejecting that amendment, the committee endorsed the president's position that "cruel treatment" is defined as treatment that rises to the level of torture. The Schiff-Flake language defined treatment as anything "cruel, inhumane and degrading."

Ahead of the White House meeting, Senate negotiators were swapping proposals with administration officials. Senate Majority Leader Bill Frist suggested that those opposed to the Bush administration plan don't have the votes to get their dissenting proposal through the Senate, and could face a bill-ending filibuster.

"Without the votes to pass their plan through the Senate, these senators have been good enough to sit down with the administration ... to find common ground," Frist said in a statement delivered on the Senate floor. "I am hopeful that very soon agreement can be reached with the president and the majority of Republicans."

One of the Republicans leading the battle against the administration on the detainee issue, Arizona Sen. John McCain, did not answer direct questions about negotiations at a breakfast meeting in Washington, D.C., and only briefly mentioned the debate during remarks at the meeting.

"There's an honest difference of opinion with the administration, but we're all still friends," McCain said.

The administration is seeking to clarify the Geneva Conventions over its vague language about detainee treatment. McCain warned against making modifications, saying the problem with doing so lies in instances when foreign countries capture U.S. soldiers and wish to modify the Geneva Conventions for their own purposes. Citing a letter written last week by former Secretary of State Colin Powell, McCain said that U.S. would lose moral authority by changing the conventions.

"Literally every military leader in the last 50 years objects strenuously to modifying the Geneva Convention," he said.

McCain said that negotiations were proceeding over changing the War Crimes Act, which is different from the Geneva Conventions, but would still give CIA interrogators "the latitude they need."

"We're working very hard with the administration and I think we're making progress to try and amend the War Crimes Act, which is not a treaty it's a piece of legislation, so that we can give these people a lot of the latitude they need and give them the protection from criminal and civil liability and still get the job done," he said.

The chief Senate negotiator called the discussions that began late Monday "constructive."

Senate Armed Services Committee Chairman John Warner, R-Va., declined to discuss the White House offer sent to Capitol Hill. A revised Senate response was sent back to the White House on Tuesday.

Warner said he held a "ray of optimism" that an agreement would come soon. "We're at a juncture in negotiations" and "progress is being made in good faith," Warner told reporters.

Another Senate source said the White House had offered some "interesting ideas."

In the meantime, Senate Judiciary Committee Chairman Arlen Specter and the committee's top-ranked Democrat, Patrick Leahy, said they want to take up the bill that came out of Warner's committee last week, which could lead to more changes in the bill. It will be up to Frist to decide if they are allowed to do so.

In a letter to Frist on Wednesday, Specter of Pennsylvania and Leahy of Vermont said they were interested in reviewing the war crimes and habeas corpus provisions in the bill. Habeas corpus is the right to have a detention reviewed by a court.

Frist, of Tennessee, didn't reveal any new language but said he sees progress in the negotiations.

"I'll have to say that over the last 24, 36 hours, I'm encouraged by the efforts that are underway to negotiate and to achieve a common ground," Frist said Tuesday.

Common ground among Republicans and the Bush administration on interrogating detainees already exists to some degree. Everyone involved in the discussion says they recognize that Common Article 3 of the Geneva Conventions — which prohibits "outrages upon personal dignity, including humiliating and degrading treatment" — is far too vague to give the CIA clear legal standards for interrogating high-value terrorists with knowledge of future terrorist plans.

"We have an urgent duty to learn who they are and where they are what they are doing and to stop them before they can act," Vice President Dick Cheney said Tuesday about the administration's terror-fighting tactics.

"The best source of information, obviously, is the terrorists themselves. We've obtained extraordinarily valuable information through the detainee program, including from Khalid Sheik Mohammed, the mastermind of 9/11," Cheney said.

To some negotiators, the question that divides negotiators comes down to who should be left to interpret the vagaries found in the conventions.

"You know, somebody's going to interpret what Common Article 3 means. It is either going to be some European court or it's going to be the U.S. Congress and the U.S. courts," said Sen. Mitch McConnell, R-Ky.

Foreign courts have ruled that degrading treatment for prisoners includes everything from having to share an open toilet to loud music and sleep deprivation. The administration proposed language written by Sen. John McCain, R-Ariz., in last year's Detainee Treatment Act, establishing the protections in the U.S. Constitution against cruel and unusual punishment, as the standard for interrogating imprisoned enemy combatants.

"It is quite specific, quite specific," McConnell said of the rules outlined for CIA interrogators. "That is the kind of certainty that (CIA Director) General Hayden is looking for so he can assure his people that they can once again engage in detainee interrogation."

But along with others, McCain refuses to apply his own language to the newest situation, saying that would be a redefinition of the Geneva Convention decades after it was ratified.

Attorney General Alberto Gonzales said he believes some people have the misperception that the president's proposal would signify "a retreat" from the Geneva Conventions, but "nothing could be further from the truth."

"We're trying to work with Congress to see whether or not we can achieve both objectives of, again, allowing the commander in chief to gain information from the enemy to protect America but to do it in a way that makes it quite clear that of course we are not retreating in any way from our obligations under the Geneva Convention," Gonzales said.

Other senators also insist the CIA must be given some sort of clear guidance on interrogations.

"We've got to be sure that this political moment, we don't make a mistake and tie the hands of CIA people that are out trying to protect the lives of American people," said Sen. Jeff Sessions, R-Ala.

A tight wrap on the compromise language suggests that both sides are serious about reaching a compromise. One Senate source said of negotiations with the White House: "There is a way forward, and we'll help them find it."

That would also be an aid to lawmakers who want to get the bill finished. House and Senate leadership have delayed plans for a floor vote on the administration's plan, with House Majority Leader John Boehner, R-Ohio, rescheduling a Wednesday vote so that the Judiciary Committee could further review the bill. A congressional official speaking on condition of anonymity told the Associated Press that House leaders were uncertain they would have enough votes to pass the Bush plan.

House Intelligence Chairman Peter Hoekstra, R-Mich., said he had not been briefed on late-night negotiations between Republican senators and the White House, but he expected significant differences between any bills passed by the House and Senate.

Yet "if the Senate and the White House have reached an agreement, that is probably what would end up becoming law and making its way to the president's desk," Hoekstra said at the conservative American Enterprise Institute think tank.

The White House has said in its current form, the Senate version passed last week in committee would put an end to the CIA interrogation program. McConnell said regardless of the negotiations, the bottom line is that "the terrorist interrogation program can go forward."

Asked how problematic it would be if the Senate did not deliver a bill before Congress leaves Washington to campaign for the November midterm, Sen. Lindsey Graham, an opponent of the administration language, warned it would be bad news.

"It will be terrible for our troops," said the Air Force reserve attorney. "I'd like to try one of these guys (detainees) in my lifetime. We're doing a better job of keeping them out of court than their own lawyers. ... If we keep pushing the envelope, we're never going to get this done."

FOX News' Jim Angle, Trish Turner and Molly Hooper and The Associated Press contributed to this report.