WASHINGTON — President Bush’s decision to send 21,500 more troops to Iraq has members of his own party scared that the strategy could fail and cause voters to turn on Republicans in 2008 in a replay of the midterm elections.

Mr. Bush, outlining his troop buildup in a prime-time address last night, said a beefed-up American force will restore order to Baghdad and provide incentives for Iraq’s government to step up home-grown security measures.

Publicly, most Republican leaders have closed ranks around the commander-in-chief, asserting the troop infusion is a short-term step that deserves a chance to work. Yet some Republicans who have rallied around the White House in the past are now distancing themselves from the buildup.

“A troop surge would put more American troops at risk to address a problem that is not a military problem,” Senator Coleman of Minnesota, a Republican on the Foreign Relations Committee, said in a speech Wednesday.

“I oppose the troop surge in Baghdad because it is not a strategy for victory,” Mr. Coleman, who faces a potentially tough re-election in 2008, said.

Senator Brownback of Kansas, who is exploring a run for the Republican presidential nomination, has also broken ranks. “I do not believe sending more troops to Iraq is the answer,” Mr. Brownback said Wednesday in a statement. “Iraq requires a political rather than a military solution.”

Rep. Heather Wilson, a Republican of New Mexico and an Air Force veteran, also voiced doubts after Mr. Bush’s speech. “I’m skeptical that this strategy will work,” she said in a telephone interview.

Senator Smith of Oregon is another buildup opponent. “We’ve done surges before, and they’ve gotten us nowhere,” he said in an interview this week.

“I’m skeptical about another unless there’s some redefinition of victory that I haven’t heard yet.” Mr. Smith, a Republican, also faces re-election in 2008.

Ms. Wilson, who survived a tough House re-election race in November, sent Mr. Bush a letter on January 8 after an Iraq visit in which she expressed reservations about a troop spike. “No one I have talked to can explain to me,” Ms. Wilson wrote, “why we should expect increasing U.S. forces in Baghdad at the levels being discussed would have a different outcome now than it has last summer and fall.”

Republican congressional leaders, who were among a large group of lawmakers Mr. Bush met with this week, took a far more positive view of the administration’s retooling of its Iraq strategy.

The Senate minority leader, Senator McConnell of Kentucky, called Mr. Bush’s measures “courageous and correct” and said the strategy will “give us a chance for victory.”

The House minority whip, Rep. Roy Blunt of Missouri, said it isn’t the job of members of Congress “to dictate strategy to the commander-in-chief, who is ultimately responsible” for carrying out a winning strategy. “I was pleased to hear the president repeat what he has told the Iraqi leaders: The Iraqis must be principally responsible for Iraq’s future,” Mr. Blunt said in a statement.