For House Republicans, the debt ceiling debate has come down to a simple question: Do they trust Speaker John Boehner?

“You either trust the Speaker or not. I do,” Rep. Tom Cole (R-Okla.) said of the Ohio Republican on Monday.

“This is a test for the Republican Conference, not the Speaker. Can we trust the guy we elected unanimously to lead us” to now cut the best possible agreement with Democrats, Cole added.

With one week left before the Treasury’s Aug. 2 deadline to avert government default, lawmakers continued their game of political and procedural chess, with no clear path to the checkmate.

House Republicans released a package that would raise the debt ceiling immediately by $1 trillion in exchange for $1.2 trillion in cuts, even though President Barack Obama has said he would not support a plan that does not extend the limit through 2013. Senate Democrats introduced an administration-backed plan with $2.7 trillion in savings, with no revenues and no entitlement reform.

Under pressure from tea party activists and other conservative organizations, Boehner and his top lieutenants cannot afford to pass a deal that does not have significant GOP support, and in the end, more Republicans than Democrats will have to vote for a debt and deficit package.

But Boehner has had to distance himself repeatedly from Obama, even as he attempts to craft a deal that can secure the president’s signature and avert a potentially catastrophic default on the nation’s debt obligations. After walking away from a deal with Obama for the second time Friday night, Boehner found himself still battling suspicion among his rank-and-file Members over whether he is crafting an agreement with the president and not them. During a conference call Sunday, Boehner said, “There are no secret negotiations going on, so don’t worry,” according to a source familiar with the call.

That call was intended as a plea for Conference unity, but reviews of the Boehner legislation were mixed coming out of a Monday afternoon meeting on the deal.

Like many of her GOP colleagues, Rep. Marsha Blackburn (Tenn.) praised Boehner’s efforts. But, as was the case with most, Blackburn declined to specifically back the measure, saying she is “waiting to take a look at what it says. … Let’s read the bill. It’s always good to read the bill.”

House Ways and Means Chairman Dave Camp (Mich.), who said he would vote for the measure, praised Boehner’s work.

“I think it’s a plan that’s true to our principles, having the cuts being larger than the increase in the debt limit … [and it] has structural reform and no tax increases, so I think it’s a solid plan that’s true to the principles we’ve laid out for many weeks now.”

Other Republicans, however, were already coming out against the bill.

In a statement, Republican Study Committee Chairman Jim Jordan (Ohio) rejected the plan outright.

“While I thank the Speaker for fighting for Republican principles, I cannot support the plan that was presented to House Republicans this afternoon,” Jordan said.

“The Senate should resume debate on the Cut, Cap, and Balance Act, amend it if necessary, and pass it, so we can provide the American people a real solution,” he added.

Rep. Tim Huelskamp (R-Kan.), a freshman conservative, also issued a statement in which he said he would not support the bill.

It is unclear how deep distrust of Boehner’s plan goes. Only nine Republicans voted against the Cut, Cap and Balance bill last week, and only 39 Members have signed a pledge that commits them to supporting a debt limit increase only if a balanced budget amendment has first been passed. The chances of such a constitutional amendment clearing both chambers this year are dim.

Cole downplayed opposition to Boehner’s plan, asserting, “This is a potentially career-defining vote … so in those situations you always have to talk Members through” them.

Cole also said that unlike during the fight earlier this year over government funding and a continuing resolution, Boehner has “a united leadership behind him. It’s very important that he has [Majority Leader] Eric Cantor [R-Va.] behind him; it’s very important that he has [Majority Whip] Kevin McCarthy [R-Calif.] behind him.”

Still, that sort of trust is not necessarily a given for Boehner. Unlike Minority Leader Nancy Pelosi (Calif.), who had a tight grip on her majority during her run as Speaker, Boehner has opted for a more open approach to leadership.

While some had thought a looser form of leadership would help the Conference mature quickly, it has instead given running room to conservatives who have proved to be a problem for Boehner’s leadership style throughout the debt ceiling talks. In fact, outside organizations were already ramping up their opposition to Boehner’s plan Monday afternoon.

In a statement, the Cut, Cap and Balance Coalition, which was instrumental in pushing the GOP to back its plan in the first place, rejected Boehner’s proposal.

“To be clear, we are not criticizing the Speaker; however, we cannot support his framework, and we urge those who have signed the Pledge to oppose it and hold out for a better plan,” the group said.

While Boehner attempts to sell his plan to stubborn conservatives, Senate Democrats introduced an administration-backed plan with $2.7 trillion in savings, with no revenues and no entitlement reform. Senate Majority Leader Harry Reid (D-Nev.) said Monday that he would start the time-consuming procedural processes to have a vote on the package this week.

But time constraints threatened Senate action, especially considering the Reid bill has already been declared a nonstarter in the House.

Because any one Senator can hold up legislation, staging a filibuster is “one possibility” and “something that’s come up in conversation and is being considered,” said a GOP aide to a conservative Senator. The aide added a caveat: “Considering things are so liquid now, until there’s more hard information, I don’t think it’s fair to speak to whatever the tactics will be.” A spokesman for Senate Minority Leader Mitch McConnell (R-Ky.) would not say whether the leader was explicitly discouraging Members from filibustering.

Senate Republicans caucused Monday evening to review their budget options, sources said. Earlier in the day, McConnell took to the floor to express support for the Boehner plan. But he also did not explicitly dismiss the Reid plan.

Reid will need Senate Republicans to pass his proposal, which Democrats plan to attach as an amendment to a pending, nonbinding Sense of the Senate resolution. Democrats believe the $2.7 trillion plan should pass muster with Boehner, whose two major demands were that any lifting of the debt ceiling be matched dollar for dollar with spending cuts and that it not touch revenues. Both the Reid and Boehner plans include an outline for a joint committee to find further deficit savings in the future.

When asked whether he believed he would have the votes to send his plan to the House, Reid said: “I would hope so. I’m giving them what they want.”

A Republican Senate aide indicated that even though there were two separate legislative tracks for a debt limit solution, ultimately, the path to averting default would start in the House and end in the Senate.

“The Reid approach cannot probably pass the House; therefore, it’s a nonstarter,” the aide said.

But for many conservatives and tea party loyalists on both sides of the Capitol, neither proposal hit the mark in reducing the deficit.

“The proposed deals being discussed today by House Republican and Senate Democrat Leaders do not make cuts to our debt. They do not solve our debt problems. They do not balance the budget, ever,” Sen. Rand Paul (R-Ky.) said.