Republican strategists said they were not surprised about the poll’s findings, though they said Republicans were too pessimistic in concluding now that the party could not win in 2008.

“People should be concerned — we’ve had a tough last year and a half or so,” said Glenn Bolger, a Republican strategist. “But if you go back in time to 1991, the Democrats had a lot of the same concerns, both about the candidates running and their possibility of winning. And it turned out pretty well for them.”

The national telephone poll was conducted Wednesday through Sunday with 1,362 adults, including 698 Republicans. The margin of sampling error for all adults is plus or minus three percentage points and four percentage points for Republicans.

The poll also found an increase in approval of the way Mr. Bush is managing the war in Iraq, to 28 percent from 23 percent, and how he is handling foreign policy. But at a time when the administration has come under fire for the way veterans from Iraq have been treated at Walter Reed Army Medical Center, 76 percent of Americans, including 57 percent of Republicans, said the Bush White House had not done all it could to deal with the needs and problems facing returning military personnel.

The poll suggested that opinions were still fluid about three of the leading Republican presidential contenders. Mr. Giuliani is the best known of the candidates, but 41 percent of Republicans said they had not formed an opinion of him; 50 percent said they had a favorable rating of him, compared with 9 percent with an unfavorable view of him.

Fifty percent of Republicans said they did not know enough about Mr. McCain to offer a view on him or were undecided, even though he is running for president for a second time. Of the remainder, 32 percent said they had a favorable view of him, compared with 18 percent who said they had an unfavorable view.

By a margin of 43 percent to 34 percent, Republican primary voters said they would prefer to see Mr. Giuliani win the nomination over Mr. McCain, but those kind of measurements taken this early in a campaign tend to be largely discounted by professional pollsters.