WASHINGTON (CNN) -- In a closed-door strategy session Tuesday, Senate Republican leaders made a "cold assessment" of the situation involving U.S. Attorney General Alberto Gonzales and determined that while he may have "bungled" the response to criticism of the fired U.S. attorneys, he didn't do anything wrong and he should not be pushed out, CNN has learned from two Republican sources who were in the meeting.

One source said that while Gonzales is very close to President Bush he has "made no friends with Republicans" on the Hill and has "no good will here." But "our guys work on principle" and "they don't see this as enough to get him out," one of the sources said.

"What they've done and how they've handled this is stupid," the same source said. "But not, 'oh God, we got to get this guy out of here.'"

This assessment by the GOP leadership -- which is headed by Senate Minority Leader Mitch McConnell of Kentucky, Senate Minority Whip Trent Lott of Mississippi and GOP Conference Chair John Kyl of Arizona -- may differ with that of many rank and file Republicans in the Senate, particularly moderates.

CNN interviews with close to a dozen Senate Republicans Tuesday paint a picture of stress and anxiety over the matter by senators, many of whom say Gonzales's credibility has been severely damaged.

"I think there are issues of confidence that have to be addressed," said Sen. Norm Coleman of Minnesota, a moderate facing re-election in 2008.

"It's deeply disturbing," said Sen. Olympia Snowe, R-Maine, another moderate. "Time is of the essence. The sooner they come up and testify and get all the facts on the table the better off the country will be."

"I think he lost a lot of credibility last week," said Sen. Lisa Murkowski of Alaska. "His credibility continues to erode and I think it makes it a very difficult situation to do his job."

Sen. Susan Collins of Maine, another moderate up for re-election in 2008 said she "didn't think he has served the president very well but it's up to the president whether or not he continues in the position."

Sen. Gordon Smith of Oregon said many senators are reluctant to call for Gonzales's firing publicly but have started saying privately in the cloakroom that it's time for him to go. "Many senators, they feel personally aggrieved by this."

Other Republicans said they wanted to wait until all the facts got out before deciding if Gonzales should go.

"I'm not going to be stampeded into making a decision," said Sen. Lindsay Graham, R-South Carolina, who is also up for re-election in 2008 and who has complained the White House handled the matter "clumsily." "I'll listen to what he has to say," Graham said.

Graham said President Bush may have help Gonzales, at least for a while, when he called the attorney general Tuesday morning to express his confidence in him. "I think it stops the stampede mentality a little bit."

Sen. John Cornyn of Texas, a reliable White House supporter, said the administration needs to release "all the facts" in order to quiet its critics.

"I think the intrigue and conspiracy theories that are feeding this thing are making it worse than it would otherwise be."

Cornyn and Graham echoed another complaint of many Senate Republicans: the role of Chuck Schumer, D-New York, as the Democrats point man on the scandal.

"That's where this thing crosses a very bad line," Cornyn said. "I think it begins to discredit the whole investigation because the first thing Democrats want to do --particularly Chuck Schumer the chairman of the Democratic Senatorial Campaign Committee -- is get Karl Rove under oath in the committee room. I mean, he is just salivating over that possibility."

-- CNN's Dana Bash and Ted Barrett