House Speaker Paul Ryan, left, and Senate Majority Leader Mitch McConnell, right. (AP Photo/Andrew Harnik)

The leaders of both the House and the Senate on Tuesday squelched hopes that Congress might pass a new authorization to fight the Islamic State, citing concerns that such a measure would tie the next president’s hands.

House Speaker Paul Ryan (R-Wis.) and Senate Majority Leader Mitch McConnell (R-Ky.) both expressed doubts during a POLITICO Playbook breakfast event that Congress could pass, and President Obama would sign, a new authorization for military force that would give the administration new tools to fight the Islamic State without imposing unacceptable limits on how to wage that fight.

“If we’re going to do an AUMF, it ought to give the president all the authority he may need,” McConnell said. “I would not want to saddle the next president with a highly prescriptive AUMF.”

“Can we write an AUMF that the president will sign where he’s not going to handcuff the next president, and can we get consensus on how to do that?” Ryan asked. “That’s where we’re at right now.”

There is currently a vast difference of opinion among members of Congress as to how the United States ought to be fighting the Islamic State. Some members have advocated sending in thousands of ground troops, while others want to keep boots on the ground to an absolute minimum.

There are also a range of AUMF proposals kicking around Congress. At least one, from Sen. Lindsey Graham (R-S.C.), would give the administration wide-ranging and open-ended authority to wage a fight against the Islamic State, while at the other end of the spectrum, a proposal from House Permanent Select Committee on Intelligence Ranking Member Adam Schiff (D-Calif.) would give the president three years to fight it, while ending the AUMFs the administration has been using thus far to justify its operations.

In principle, Ryan said that the idea of a new AUMF was “a debate worth having” and that it would potentially be “a good sign to have a new one, updating our AUMF to declare our mission with respect to ISIS.” He mentioned that House Permanent Select Committee on Intelligence Chairman Devin Nunes (R-Calif.) and House Foreign Affairs Committee Chairman Ed Royce (R-Calif.) were also open to a debate.

But both Ryan and McConnell said they believed that the president had the legal authority to conduct a war against the Islamic State under a 2001 AUMF that Congress passed after the Sept. 11 terror attacks, paving the way for the U.S. to fight al-Qaeda and affiliated groups. The Islamic State was once linked to al-Qaeda – though al-Qaeda’s formal repudiation of those ties last year have made the administration’s legal argument in favor of the existing AUMF murkier.

Ryan and McConnell’s reasoning also rests on complaints about the current administration’s anti-ISIS strategy.

Many of the potential next presidents that Ryan and McConnell are worried about hamstringing with a restrictive AUMF have advocated more expansive and intensive measures against ISIS. Democratic frontrunner Hillary Clinton has joined Republican candidates like Jeb Bush and Marco Rubio in calling for a no-fly zone in Syria — something that also has the support of many Republicans in Congress, but Obama’s administration has argued would be too costly to enforce. Some of the Republican presidential candidates have also called for more ground troops to fight the Islamic State, especially in Iraq.

Save for those differences, Obama has argued there really isn’t much daylight between his strategy and the Republican candidates’ proposals, beyond tough talk.

But in Ryan’s estimation, the AUMF proposal that Obama sent to Congress earlier this year “put too many constrictions on the military” and “handcuffed the next president.” Under the recently-passed National Defense Authorization Act, Ryan noted, there is a requirement that the president present Congress with a plan to defeat the Islamic State – once they receive it, he suggested, then it might be appropriate to start talking AUMFs again.

“Let’s see what the plan to defeat ISIS is, and that is good time to then consider whether that requires, or whether it would be in our interest, to have a new AUMF accompany a new strategy to defeat ISIS,” Ryan said.

McConnell also expressed doubts about the president’s strategy, noting that it is incumbent on the U.S. to “rally the Saudis, the Egyptians, the Emiratis to join” any effort to defeat the Islamic State and say “here’s the plan.”

But the final barrier to a new AUMF may simply be the familiar hurdle of finding a filibuster-proof majority. In McConnell’s estimation, there just aren’t the votes in the Senate to pass the kind of AUMF he would consider appropriate.

“I can’t imagine this Senate getting more than 60 votes for the kind of AUMF that the next president may need, which is the authority to do what needs to be done,” McConnell said.