White House officials fear that the last pillars of political support among Senate Republicans for President Bush’s Iraq strategy are collapsing around them, according to several administration officials and outsiders they are consulting. They say that inside the administration, debate is intensifying over whether Mr. Bush should try to prevent more defections by announcing his intention to begin a gradual withdrawal of American troops from the high-casualty neighborhoods of Baghdad and other cities.

Mr. Bush and his aides once thought they could wait to begin those discussions until after Sept. 15, when the top field commander and the new American ambassador to Baghdad are scheduled to report on the effectiveness of the troop increase that the president announced in January. But suddenly, some of Mr. Bush’s aides acknowledge, it appears that forces are combining against him just as the Senate prepares this week to begin what promises to be a contentious debate on the war’s future and financing.

Four more Republican senators have recently declared that they can no longer support Mr. Bush’s strategy, including senior lawmakers who until now had expressed their doubts only privately. As a result, some aides are now telling Mr. Bush that if he wants to forestall more defections, it would be wiser to announce plans for a far more narrowly defined mission for American troops that would allow for a staged pullback, a strategy that he rejected in December as a prescription for defeat when it was proposed by the bipartisan Iraq Study Group.

“When you count up the votes that we’ve lost and the votes we’re likely to lose over the next few weeks, it looks pretty grim,” said one senior official, who, like others involved in the discussions, would not speak on the record about internal White House deliberations.