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."