WASHINGTON – The Supreme Court nomination of White House counsel Harriet Miers faced new and urgent troubles yesterday, with speculation mounting throughout the day that at least one conservative Republican senator had made an unsuccessful attempt at getting the White House to withdraw Ms. Miers’s name altogether.

The chairman of the Senate Judiciary Committee, Senator Specter, a Republican of Pennsylvania, on Wednesday publicly expressed his dissatisfaction with responses Ms. Miers gave to a committee questionnaire about her judicial philosophy and professional work. Mr. Specter also expressed his annoyance with a disagreement he had with the nominee earlier this week over rival accounts of a private conversation about privacy.

Mr. Specter joined the committee’s ranking Democrat, Senator Leahy of Vermont, on Wednesday in asking Ms. Miers to revise her answers to the questionnaire, which Mr. Leahy characterized as ranging from “insufficient to insulting.” The two men said they wanted fuller answer to questions about her experience with constitutional matters, her past professional associations, and a lapsed membership in the Washington, D.C. bar.

Mr. Specter also said he would press Ms. Miers about their privacy conversation at the start of the confirmation hearing, which is scheduled to begin November 7.

The nominee made matters even worse when she notified the committee later that day that her law license had been suspended for non-payment of dues one other time previously while practicing law in Dallas.

President Bush defended Ms. Miers at a morning press conference yesterday by saying that she is precisely the type of person he had pledged to nominate to the court and by assuring reporters that she would answer all of the committee’s questions fully.In an apparent dig at Ms. Miers’s conservative critics, Mr. Bush said that anyone who read the responses carefully would have gleaned that her judicial philosophy is consistent with his own.

“One thing the questionnaire does show – if people look at it carefully – is Harriet’s judicial philosophy,” Mr. Bush said in a joint press conference attended by the Palestinian president, Mahmoud Abbas. “And it’s the main reason I picked her to serve on the bench, if confirmed, and that is that she is not going to legislative from the bench. She will strictly interpret the Constitution.”

Conservatives have been the most vocal critics of Mr. Bush’s selection of Ms.Miers since he nominated her three weeks ago to replace Justice O’Connor, complaining that she has no discernible judicial philosophy or conservative credentials.

And while no Republican senator has pledged to vote for or against Ms. Miers, some are said to have expressed their dissatisfaction with the nominee’s performance in private “courtesy call” meetings over the past two weeks.

The complaints have become serious enough that at least one conservative senator is said to have asked White House officials yesterday to withdraw the nominee’s name because of a growing lack of enthusiasm for Ms. Miers among Republicans in the Senate.

“I don’t know exactly what was asked, but displeasure was expressed,” a source familiar with the White House strategy on judicial nominees said. “The White House responded that it would do no such thing.”

Republican staffers, who are charged with crafting talking points and speeches of support for senators, say that morale among judicial counsels and their other staff colleagues is also low.

The White House is depending on grassroots support for the nominee to drown out conservative pundits who have been critical of the pick. It has also enlisted the support of the U.S. attorney general, Alberto Gonzales, in speaking favorably about Ms. Miers at public events.

Ms. Miers has also had a lonely Senate supporter in Senator Cornyn, a Republican of Texas, who is scheduled to hold a press conference today with a group of Texas lawyers who are backing Ms. Miers.

If conservatives team up with Democrats to thwart the nomination, they are likely to focus in on her qualifications. Some conservative supporters of Ms. Miers, though, said that tactic could backfire.

“If her critics attempt to portray her as incompetent, they risk losing their audience,” the executive director of the Committee for Justice, Sean Rushton, said. “Most Americans aren’t going to believe a former law firm managing partner, White House deputy chief of staff, and White House counsel is incompetent.”