House Intelligence Committee ranking Democrat Adam Schiff (Calif.) began circulating a new draft AUMF on Thursday.

A flurry of new proposals to authorize military force against the Islamic State are breathing new life into a longtime debate on Capitol Hill.

But even a call to action by President Obama may not be enough to get any of them through Congress.

House Intelligence Committee Ranking Member Adam Schiff (D-Calif.) began circulating a new draft authorization for use of military force on Thursday to sanction three years’ worth of hostilities against the Islamic State, al-Qaeda and the Taliban, while Reps. Scott Rigell (R-Va.) and Peter Welch (D-Vt.) introduced companion legislation to a Senate proposal that would give the administration the authority to fight the Islamic State for three years.

Those measures — along with a far more expansive and open-ended AUMF proposal from Sen. Lindsey Graham (R-S.C.) earlier this month — are part of the congressional response to the San Bernardino shootings, which has put extra urgency behind the drive to quash ISIS.

President Obama challenged Congress to come up with an anti-ISIS AUMF during a speech to the nation last Sunday, when he said that “if Congress believes, as I do, that we are at war with ISIL, it should go ahead and vote to authorize the continued use of military force against these terrorists.”

Longtime AUMF advocates seized upon that change in “tone,” if not the administration’s legal argument justifying current hostilities against ISIS, as an important signal to build momentum now for an AUMF.

But many members and even congressional leaders are balking at the idea.

“Many just don’t want to get on the record here,” said Sen. Jeff Flake (R-Ariz.), who along with Sen. Tim Kaine (D-Va.) authored the three-year AUMF that is the counterpart to the Rigell-Welch bill. “In this case with our most fundamental responsibility here in Congress, that’s just an excuse, and we need to go on record.”

The United States has thus far justified its campaign against ISIS under the 2001 AUMF that Congress passed to green-light operations against al-Qaeda and its affiliates in the wake of the Sept. 11 attacks. The administration and several influential congressional leaders have not backed off of that legal justification – despite Obama’s call for Congress to use its authority if they are serious about fighting the Islamic State.

But lawmakers promoting an AUMF said Thursday that it was incumbent on members to create a groundswell of momentum to which leaders would have to respond.

“There’s a little too much focus on the leaders,” Welch said. “The leaders need the member to demonstrate the desire and will to act.”

“We improve our likelihood of success if we’re together,” Kaine said.

But lawmakers angling for an AUMF are far from united – not on the specifics of a bill, and not on what, exactly, it should address.

Many Republicans are wary of an AUMF that would limit a president’s ability to deploy boots on the ground, while many Democrats won’t approve an AUMF without express limits on ground troops. Kaine said on Thursday that “a massive ground troop presence that would make [the war] U.S. vs ISIL is counterproductive.”

Graham has said that he could not support an AUMF that limited the president in time or scope from being able to combat the Islamic State until it was completely obliterated.

Schiff’s proposal goes in the opposite direction – while it doesn’t limit the president from using “all necessary and appropriate force” for up to three years, it would entirely replace the 2001 AUMF and the 2002 AUMF through which Congress approved hostilities in Iraq.

Schiff said in a statement that his AUMF could “bridge the divide by consolidating and unifying our use of force again ISIS, Al Qaeda and the Taliban” and provide “an expedited mechanism to accept or reject any introduction of ground troops in a combat mission.”

The measures authored by Flake, Kaine, Rigell and Welch,  meanwhile, would replace the 2002 Iraq authorization only – though they are also intended to serve as the primary measures authorizing hostilities against the Islamic State.

They reminded reporters on Thursday that theirs is the only proposed AUMF that is both bipartisan, and now, bicameral – which is the type of support an AUMF will need to get through Congress.

“We’re certainly happy there are other members introducing AUMFs,” Flake added. “Whatever starts the debate and gets people realizing we’ve got to do this, it’s a plus.”