Speaker John Boehner will use this last week before a July Fourth recess to put the House on the record on Libya.

But the Ohio Republican’s developing hallmark of lengthy and open debate will be tested as he seeks to define the House’s position on military involvement in Libya without letting it interfere with a must-pass defense appropriations bill that is also scheduled for this week.

Boehner is reaffirming his grip on the GOP Conference, which has been widely critical of the administration for not fully consulting Congress on the decision to join the NATO-led effort in Libya. So far, Republicans have deferred to their leader on how best to proceed, as Boehner has tempered his exchanges with the White House to avoid complicating an international matter, but the next steps are far from clear.

“He’s in a very tough position,” said Rep. Tom Rooney, a former JAGS Corps officer and constitutional law professor who has blasted President Barack Obama for not seeking Congress’ approval on Libya.

“I am not a [Rep.] Walter Jones [Jr.] Republican, which is to be against what we’re trying to accomplish,” Rooney continued, referring to his anti-war colleague from North Carolina. “This has nothing to do with Libya. It has to do with the role of Congress, and I think you’re seeing Speaker Boehner say that more and more.”

Rooney authored a resolution earlier this month declaring that Obama had violated the War Powers Act in regard to Libya, and he supported Boehner’s earlier resolution calling on the president to provide a justification for participating in NATO-led airstrikes intended to enforce a no-fly zone and an arms embargo. Rooney acknowledged Boehner’s resolution, which passed June 3, was a more moderate approach that could have helped Obama win support among Republicans. That support, Rooney and others on Capitol Hill said, was squandered when the administration argued in a report released Friday that Congressional approval was not needed.

The report came in response to a strongly worded letter from Boehner, asking for details on the military effort and demanding the White House seek Congress’ approval. But the 30-page report further infuriated Republicans and some Democrats because it dismissed any need for Congress to sign off on the mission.

Boehner could put forth a measure as soon as this Thursday that seeks to rebuke Obama by cutting off funding for the Libyan effort, although GOP aides said Monday that details were still being worked out. It is unclear whether the House would consider legislation or a resolution, or what its contents would be.

“I think he’ll start to turn up the volume of the frustration at the White House over their stance of ignoring Congress,” said Ron Bonjean, a former GOP leadership staffer. “Every day President Obama ignores Congress, it makes it riskier and riskier for the administration.”

Despite the uptick in rhetoric that will likely include heated speeches on the floor this week, a strong vote on a defunding bill could have little effect since the Senate has yet to rally behind any position on Libya.

Several Republicans in the Senate have also taken a different approach than their House counterparts by maintaining that Obama does not need Congress’ approval for the ongoing military effort that began in March, in response to international concerns that Libyan dictator Moammar Gadhafi was attacking unarmed civilians and protesters.

“The War Powers Act is unconstitutional and not worth the paper it is written on,” Sen. Lindsey Graham (R-S.C.) said on NBC’s “Meet the Press.” “The president needs to step up his game in Libya, but Congress should sort of shut up and not empower Gadhafi.”

Sen. John McCain (R-Ariz.), who has been critical of the administration for its handling of the conflict, also maintained that the U.S. needs to continue its presence in Libya.

The Senate has been in a holding pattern, with the Foreign Relations Committee postponing hearings on the issue. Still, Senators that want the chamber to weigh in on the matter are looking for legislative avenues to ensure their voices are heard.

Republican sources said Sen. Rand Paul is contemplating a resolution calling for withdrawal and a bill demanding a declaration of war. As of Monday at press time, the Kentucky Republican had not decided how he wanted to proceed, if at all.

Anna Palmer and David M. Drucker contributed to this report.