Leading Senate Republicans on Tuesday urged the chamber to give an up-or-down vote on President Bush's embattled pick to be the next U.S. ambassador to the United Nations (search), John Bolton (search).

"In my usual non-confrontational fashion, I have urged Senator Frist to schedule a vote and get everybody on record ... I hope later this week or as soon as possible, we can schedule another vote," Senator John McCain said Tuesday.

McCain, the Arizona Republican who was instrumental in cutting a recent deal on judicial filibusters (search) that averted a showdown over judges on the Senate floor, said that Senate Majority Leader Bill Frist, R-Tenn., asked him to join the leader in a press conference urging colleagues to consider such a vote.

"If the Senate, in its wisdom, wants to vote down John Bolton, that's a verdict we can accept ... ... but the post cannot remain unfilled," McCain said.

Frist said Tuesday that negotiations regarding Bolton are underway, adding that "the other side [Democrats] is unreasonably filibustering this nomination."

In speaking to reporters, however, Frist did not appear confident he had or will have the votes to cut off debate on the nominee, although he wants a vote by week's end.

Two-thirds of the Senate must vote for cloture, or to end debate on a nominee. But only a majority, or 51 percent, of the Senate is needed to confirm or reject a nominee.

Frist said that by his count, if Sen. Arlen Specter, R-Pa., votes to end debate on Bolton, the "yes" votes still fall two short of the 60 needed to cut off debate. The "yes" tally would come to 58 but that includes votes from Democratic Sens. Mark Pryor of Arkansas, Mary Landrieu of Louisiana and Ben Nelson of Nebraska.

"It's been 200 days, and this vacancy sign [outside the U.N. ambassador post] is still blinking," Frist said.

Sen Minority Leader Harry Reid, D-Nev., said Frist on Tuesday told him that he was "being pressured to take a vote."

"I said, 'why doesn't the White House do something?'" Reid said he responded to the majority leader.

Earlier in the day, it was reported that Frist had privately indicated to the Democratic leadership that he wants a vote on the stalled nomination this week, congressional aides said.

The White House has predicted repeatedly that Bolton eventually will win confirmation.

Before the Senate broke for a brief recess last month, Republicans had fallen short of the 60 votes they needed to stop debate on the nomination and move to an up-or-down vote.

Republicans hold a 55-44 majority in the Senate, with one independent. That means several Democrats would have to side with Republicans to move Bolton forward.

Last month, Pryor, Nelson and Landrieu were the only Democrats to break ranks and support the move to have an immediate final vote.

Democratic Senate Leader Harry Reid of Nevada "is not aware that anyone is preparing to switch their votes" from last month's tally, Reid spokesman Jim Manley said Monday.

Democrats have held up the nomination because the administration has refused senators access to the names of the U.S. officials mentioned in 10 communications intercepted by the National Security Agency (search). Bolton requested the intercepted communications and Democrats want to know whether he was targeting certain U.S. officials.

Democrats also are seeking internal State Department documents concerning Bolton's use of intelligence about Syria's weapons capabilities.

Sen. Pat Roberts, the chairman of the Senate Select Committee on Intelligence, sent a letter Tuesday to Sens. Chris Dodd, D-Ct., and Joe Biden, D-Del., regarding the Democrats' request to disclose the names of the officials mentioned in the intercepts, saying that his staff has found "no evidence of abuse" in the matter.

Roberts said the issue has been thoroughly investigated by his committee and that he could not support the Democrats' request for about three-dozen so-called 'names of concern' regarding the NSA intercepts. He found reference to only six government officials that Democrats allege Bolton either sought to remove or displayed "abusive behavior" toward.

Robert also said the situation does not merit sending it to the director of national intelligence, John Negroponte, for review.

But a '"more focused request," Robert said, "may be a basis for moving this process forward, a goal that we all share. Once again, I am at a complete loss as to how your list of 'names of concern' could have grown to nearly 40."

The Kansas Republican added, however: "I stand ready to assist any reasonable effort to resolve intelligence-related matters as they pertain to Under Secretary Bolton's nomination."

Frist said Tuesday that he thinks the administration has provided all the information necessary and requested regarding the intercepts.

But Reid said Republicans aren't doing enough to break the impasse on that issue.

"We have moved the goalposts ... we've moved them closer ... [and] they're [Republicans] not even willing to play on that modified football field," he said.

Meanwhile, at the State Department, agency spokesman Sean McCormack said recent congressional inquiries questioning whether the United Nations can effectively be reformed and whether U.N. Secretary General Kofi Annan (search) is the right man for the job is just another example of how the world body needs a strong voicesuch as that of Bolton.

U.N. "Secretary General Annan has said that it's an organization badly in need of management reform, and I think that that's an issue that's important as well for the American people. It's important for the Congress," McCormack said.

"So one way to try to help move that ball down the field is to have a permanent representative up in New York and have Mr. Bolton up there working on behalf of the administration and on behalf of the American people."

FOX News' Julie Asher and Teri Schultz and The Associated Press contributed to this report.