To prove they are listening to their members House GOP leaders have scheduled a special meeting for next Wednesday just to talk about the way forward on the debt limit.
The two-hour open-mike-style meeting in the Capitol basement will be a chance, according to one House Republican aide, "touch gloves" and demonstrate that all ideas will be explored.
Given the political needle Boehner and other top leaders need to thread on the issue, it's likely this session will be the first of many over the next several months.
Conservatives insist they want additional spending cuts to federal programs without any increases in taxes if they agree to increase the country's borrowing authority.
With $85 billion in sweeping forced spending cuts from the 2011 debt deal now in effect, congressional negotiators know there is very little room left to cut discretionary programs.
Both sides know the only way to get bipartisan deal involves the GOP giving ceding on some revenue return for Democrats agreeing to significant changes to entitlement programs like Social Security and Medicare.
But for now, House Republicans are simply focused on an internal strategy. One idea is to link the debt ceiling vote with an overhaul of the tax code, a big priority for the GOP.
"We're open to any avenue that leads to tax reform," Sage Eastman, a top aide to Rep Dave Camp, R-Michigan, who chairs the House tax writing panel.
It's unclear how workable linking fights over popular tax deductions to an already politically complicated issue could happen in a short time frame.
While not quite endorsing that idea, Boehner alluded to that concept of dealing with both issues it at his weekly press conference when asked about how the GOP will approach the debt ceiling fight.
"We also know we can't cut our way to prosperity. We need real economic growth. And that's why you continue to hear a lot of discussion about tax reform, regulatory reform, that would help us produce more economic growth here in our country. We do both, we can begin to solve this problem," Boehner said.
Several House GOP aides say there are other ideas to round up Republican votes, such as attaching the debt ceiling vote to another "must pass" bill like the next continuing resolution to fund the government.
Another option is to combine it with legislation to allow the construction of the Keystone pipeline, an initiative pushed by Republicans that has become an environmental and political flashpoint with the Obama administration.
As is custom on Capitol Hill, it's unlikely the outlines of any potential compromise will emerge until right before the deadline this fall.
But House Republicans are considering a vote on their own plan as early as July because they know Obama and congressional Democrats will want to use the August summer recess to shape the public debate and pressure them to agree to some new tax increases.