WASHINGTON — Ever since President Obama ordered American warplanes to begin bombing terrorist targets in Iraq and Syria last year, members of Congress have insisted on having a say in the matter. The president, they declared, could not, or at least should not, take the country back to war without the input of the nation’s elected representatives.

Now, six months after he sent the military back into combat to take on the terror group calling itself the Islamic State, Mr. Obama has acquiesced and sent a measure to Congress asking it to formally authorize what he has been doing all along. And now that they have gotten what they asked for, few in Congress seem all that enthusiastic about the prospect.

One side thinks the president’s request for war-making powers is too brazen and even reckless. The other side thinks it is too spineless and probably ineffectual. “It does not seem to have resonated with anyone,” said Senator Susan Collins, Republican of Maine and a member of the Intelligence Committee. “I haven’t found any colleague who’s been enthusiastic about it.”

Some senior lawmakers even wondered aloud on Thursday whether Congress would pass any version of an authorization to use military force, or A.U.M.F. “I think when people look at 10,000 feet up, everyone says they want an A.U.M.F.,” said Senator Charles E. Schumer of New York, a member of the Democratic leadership. “When it comes to actually passing an A.U.M.F. that pleases enough people to get a majority, it’s very hard.”