“The politics of Iraq are going to change dramatically in the general election, assuming Iraq continues to show some hopefulness,” said Michael E. O’Hanlon, a senior fellow at the Brookings Institution who is a supporter of Mrs. Clinton’s and a proponent of the military buildup. “If Iraq looks at least partly salvageable, it will be important to explain as a candidate how you would salvage it — how you would get our troops out and not lose the war. The Democrats need to be very careful with what they say and not hem themselves in.”