WASHINGTON — Responding to growing concern among war-weary constituents about the purpose and cost of the U.S. mission in Libya, senators are poised to debate whether to send President Barack Obama a message that he needs to be more specific about his goals there.

Obama defended his policy Tuesday during a joint news conference in Washington with German Chancellor Angela Merkel.

“Chancellor Merkel and I share the belief that (Libyan leader Moammar) Gadhafi needs to step down for the sake of his own people,” Obama said.

“And with respect to the pace of the operations and participation, I think if you look at where we were three months ago and where we are now ... or two months ago, and where we are now, the progress that has been made in Libya is significant.”

But on Capitol Hill, senators returning from a 10-day Memorial Day recess reported that their constituents want Congress to examine more closely the U.S. involvement in Libya, as well as Afghanistan and Iraq.

The House of Representatives last week approved a measure requiring Obama to report back to Congress on Libya by later this month. In a vote last month, it turned back by a 215-204 margin a bid to expedite U.S. withdrawal from Afghanistan.

Libya is the immediate Senate concern, and Thursday the Senate Foreign Relations Committee plans to discuss legislation that will test Obama’s Senate support.

The president made it clear Tuesday that he’s not backing down in his effort to oust Gadhafi.

“The chancellor (Merkel) and I have been clear: Gadhafi must step down and hand power to the Libyan people. And the pressure will only continue to increase until he does,” Obama said.

Senate Foreign Relations Committee Chairman John Kerry, D-Mass., and Sen. John McCain, R-Ariz., the top Republican on the Senate Armed Services Committee, are pushing a measure that would express Senate support for the U.S. military mission in Libya. Obama said in a letter last month to congressional leaders that he backed such a resolution.

A full debate is expected next week.

“We’re going to have lots of opportunities to vote on different things on how people feel about Libya,” said Senate Majority Leader Harry Reid, D-Nev. “I’ll be happy to look at every different idea people have.”

There appear to be two major concerns among senators, one involving the extent of the mission, the other involving its cost.

“My concern is that the president didn’t address major questions from the onset, like what’s the endgame, or what is our exit strategy. I have yet to see any evidence of those questions answered,” said Sen. Olympia Snowe of Maine, a moderate Republican who’s up for re-election next year.

“I think it’s fair to say there are a lot of different points of view,” added Sen. John Thune, R-S.D. “There’s been a lack of clarity on missions and objectives.”

Obama supporters also want a debate.

“My strong inclination is to support what the president has done. However, a debate on the floor would add value and understanding,” said Sen. Mark Udall, D-Colo.