Sen. Lincoln Chafee, R-R.I., said he is troubled by Bolton's behavior and wants to discuss it with other Republican senators.
Earlier, Chafee had said he would vote for Bolton, albeit with reservations. He sits on the GOP-led Senate Foreign Relations Committee, which is considering Bolton's nomination, and could deny Bolton the panel's recommendation with a "no" vote.
"We need to talk about it. I want to hear what (colleagues) have to say," Chafee said.
The White House "has been in touch" to lobby him, he added.
Two other Republican committee members, Sens. George Voinovich of Ohio and Chuck Hagel of Nebraska, have also expressed reservations about Bolton's nomination.
"John Bolton is in some serious trouble on Capitol Hill," said CBS News National Political Correspondent Gloria Borger.
"There are three senators on the Foreign Relations Committee that are now saying the Republican Caucus ought to get together to talk about John Bolton. There are questions about his temperament, there are questions about whether he is so ideologically driven that he tried to get people transferred who gave him intelligence information that he didn't like. So, I do think he's in some real trouble," said Borger.
Mr. Bush blamed partisan bickering in the nation's capital — "where sometimes politics gets in the way of doing the people's business" — for a delay in the committee's vote on Bolton's nomination, even though that delay came about only because some Republicans have joined Democrats to force it.
"John's distinguished career and service to our nation demonstrates that he is the right man at the right time for this important assignment," Mr. Bush said. "I urge the Senate to put aside politics and confirm John Bolton to the United Nations."
Allegations of abusive personal behavior and possible instances of misuse of his government power derailed a key vote by the committee on Bolton on Tuesday. A new vote is probably three weeks off, giving Democrats time to investigate new charges and the White House time to lobby disaffected Republicans.
Mr. Bush's impromptu remarks, which came at the top of a planned speech in Washington before a meeting of the Independent Insurance Agents and Brokers of America, were clearly designed to show that the White House is not giving up on Bolton.
Mr. Bush called his nominee "a good man."
Democratic senators are seeking new information about whether Bolton abused his authority and misled a Senate committee.
The Senate Foreign Relations Committee asked Wednesday to interview former deputy CIA director John McLaughlin, another unidentified CIA official and a National Intelligence Council official, a Democratic committee staff member said. The staff member spoke only on condition of anonymity because the investigation is still under way.
The three spy officials had been scheduled to meet with Bolton in July 2002 when Bolton was in the midst of a bureaucratic disagreement with a CIA analyst. Bolton told the committee last week that he never tried to get the analyst fired, and he implied that he had dropped the matter quickly. The analyst was not fired.
Sen. Christopher Dodd, D-Conn., asked McLaughlin and the two officials whether they met with Bolton and whether he discussed removing the analyst from his job, a Dodd aide said.
Government records dispute Bolton's account of the visit to the CIA, according to Sen. Joe Biden, D-Del., and the new inquires are partly an attempt to find out whether Bolton lobbied top officials to get rid of the analyst.
Separately, Sen. Jay Rockefeller of West Virginia, the top Democrat on the Senate Intelligence Committee, is asking the National Security Agency for details of intelligence requests made by Bolton, Rockefeller spokeswoman Wendy Morigi said.
At the same time, there are efforts to counter the stream of allegations. The Associated Press obtained a letter from a Virginia businessman disputing a former colleague's graphic description of an irate Bolton throwing things at her and pounding on her hotel room door during an international conference a decade ago.
The White House vigorously defended Bolton on Wednesday, predicting he will be confirmed.
The White House also offered to arrange private meetings between Bolton and any wavering Republicans, though White House press secretary Scott McClellan said that the president himself was not personally lobbying GOP lawmakers. There was no indication that Bolton might withdraw.
Democrats are also seeking more information on other personnel incidents involving Bolton.
"Senate Democrats on the committee continue to bring up these allegations that are unsubstantiated, that are unfounded, that John Bolton has addressed in his testimony" before the committee, McClellan said.