Speaker of the House John A. Boehner (R-Ohio), right, said any effort to approve President Obama's war resolution has fizzled. (Joshua Roberts/Reuters)

House Speaker John A. Boehner (R-Ohio) declared an impasse at efforts to craft a new war resolution to take on Islamic State forces, suggesting the only chance for its approval would be President Obama pushing for a more robust U.S. military engagement in Iraq.

"Until the president gets serious about fighting the fight, until he has a strategy that makes sense, there’s no reason for us to give him less authority than what he has today, which is what he’s asking for," Boehner told a group of reporters Tuesday, following his trip with lawmakers to several Middle East hot spots during the congressional recess.

Boehner blamed “artificial constraints” on the 4,500 American trainers and advisers to the Iraqi army, suggesting that a slight increase in U.S. troops could occur if the Pentagon’s commanders suggested they were needed to help direct fighting against Islamic State forces. "They’re only there to train and advise the Iraqi army, and the fact is it’s just that – training and advising,” he said, dismissing fears that his proposal would lead to tens of thousands of additional U.S. troops locked in another bloody ground war.

“There’s more that we can do, with limited risk, and it wouldn’t require that many more people," the speaker said.

Boehner's comments expanded on similar views from House Majority Leader Kevin McCarthy (R-Calif.), who on Monday said there was not enough support for the original war resolution sent to Congress by Obama earlier this year. White House officials rejected that position and said that it was a result of the dysfunctional Republican caucus in the House.

"It’s his responsibility to count votes," White House press secretary Josh Earnest said Monday of McCarthy's view. "I don’t think anybody’s batting a thousand when it comes to votes up there, so we’ll see."

[Here's the full text of Obama's proposal for a new authorization for the use of military force.]

The White House proposal, submitted in February after months of bipartisan clamor from lawmakers demanding a role in the new war front, included a prohibition against "enduring offensive ground combat operations" in a formal authorization for use of military force, AUMF. It was limited to three years, effectively replacing the 2002 AUMF that approved the Iraq war.

Those restrictions appealed to Obama's instincts as an anti-war candidate for president in 2008, as well as to the many Democrats who were opposed to the Bush White House's handling of Iraq operations. However, with Republicans now in control of the House and Senate, those limitations on U.S. forces have left little support among the increasingly powerful hawkish wing of the GOP.

Without any action from Congress, Obama can continue to wage the fight however he sees fit. Which, Boehner has decided, is a better option than trying to work with the draft that White House officials sent up to Capitol Hill.

“The president’s asking for less authority than he has today. I’ve never seen any president, ever, do this," he said, adding that he does not want his own committee chairmen to work up their own AUMF. “As much as I think Congress ought to speak on this issue, it’s going to be virtually impossible to do that."