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Mr. Keene estimates that “perhaps 15 percent of conservatives and more Republicans share Hagel’s position even today, and that could make him a factor, especially if the ‘bad’ news out of Iraq continues.”

Mr. Gilmore disputes Mr. Hagel’s conservative credentials.

“Hagel is the fourth addition to the cluster of moderate candidates that include Rudy Giuliani, Mitt Romney and John McCain,” Mr. Gilmore said. “They will be dividing up the small minority of moderate vote in the GOP.”

Mr. Keene thinks Mr. Hagel has a far different image problem. “He is seen as opposing an incumbent president of his own party during wartime and, I think, his perhaps naive faith in international institutions and solutions.”

“He would make the race more interesting but would have an incredibly difficult time appealing to the GOP base at this time,” Mr. Keene said.

Mr. Hagel is regarded as an ideological soulmate of Arizona Sen. John McCain on changing campaign-finance rules and other issues, but Mr. McCain has become as strong a supporter of increasing the U.S. force in Iraq while Mr. Hagel is a doubter. Meanwhile, both men’s conservative ratings plunged last year.

Mr. Hagel’s American Conservative Union rating for 2006, posted on ACU Web site yesterday was 75, down 21 points from his 2005 score of 96. He voted contrary to conservative positions on defining earmarks in appropriations bills, on allowing “native” Hawaiians to form a government within the broader state government, and on immigration and border-enforcement changes, among other things.