Susan Walsh / AP House majority leader Eric Cantor speaks to reporters in Washington on July 11, 2011

At his press conference on Monday, President Obama made clear that his frustration with House Republicans’ intransigence in negotiations to raise the federal borrowing limit did not extend to their leader. “I think Speaker Boehner has been very sincere about trying to do something big,” Obama said, one of several compliments he paid in an extended embrace of his negotiating partner. “The politics that swept him into the speakership were good for a midterm election; they’re tough for governing.”

Tough indeed. And a death hug from a polarizing Democratic President doesn’t make the task easier for John Boehner. From the start of his speakership, Boehner has been forced to contend not just with a fractious band of freshmen who would rather risk economic catastrophe than give ideological ground but also with a top lieutenant positioning himself as Boehner’s purist foil. While Obama may respect Boehner’s forthrightness, recent twists in the plot of the debt-ceiling negotiations suggest that if he wants to persuade hard-line House conservatives not to jeopardize the nation’s economy, he may have been negotiating with the wrong Republican.

During a high-stakes summit at the White House on Sunday, Eric Cantor was the primary voice speaking on behalf of Republican interests, according to several accounts of the meeting. A senior Democratic aide briefed on Monday’s talks tells TIME that Cantor again “dominated” much of the negotiations on the Republican side, while Boehner “hardly spoke.”

Cantor’s stated resistance to a grand bargain freighted with revenue increases — and the perception that his position reflects the pulse of the GOP conference — likely influenced Boehner’s decision to scuttle his pursuit of a “big deal” with Obama. Weeks earlier, Cantor’s abandonment of Biden-led negotiations were the death knell for those talks. Speculation about palace intrigue is a Washington tradition, but the rumored frost between the top two Republicans in the House could have significant impact on whether the two parties can craft an agreement to raise the debt limit by Aug. 2. That’s particularly true if personal ambition leads the lawmakers to elevate political calculations over policy imperatives.

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During a meeting with reporters on Monday afternoon, Cantor dismissed the characterization that a rift had opened between Boehner and his No. 2. “I know you all love to write the soap opera here,” Cantor told a standing-room-only crowd in the Capitol, but “the Speaker and I are on the same page.” It was the first question he was asked, and he later repeated his answer. Less than an hour later, before the two leaders trekked to the White House for another round of negotiations, Boehner held his own briefing with the press and paid tribute to hard-line Republican demands — a balanced-budget amendment, binding spending caps to stem a slide back to profligacy — and wagged his finger at a reporter who asked about his apparent retreat to the safety of the pack. “There were no tax increases ever on the table,” Boehner insisted.

But while Boehner said on Monday that a bill that raises taxes cannot pass the House, it is Cantor who has made every effort in recent days to stake out the anti-tax ground. Helping to thwart Boehner’s push for a big deal was only the latest jockeying between the supple, dealmaking Speaker and his pugnacious top lieutenant. By tapping Cantor as an emissary to the Biden negotiations, Boehner tried to gain Cantor’s imprimatur for any deal it yielded; by stalking out over tax increases, Cantor cleaved separation, as he did again by pushing for a smaller deal at a Thursday meeting at the White House. The House majority leader, who didn’t support Boehner’s bid for that job in 2006, could be poised to capitalize should an intraparty feud over the debt limit spark an insurrection. “I think what we learned over this past weekend is that John Boehner … is not really Speaker of the House,” New York magazine political columnist John Heilemann says. “Eric Cantor is the Speaker of the House.” Pointing to the potency of Cantor’s anti-tax vehemence, Darrell West of the Brookings Institution said on Monday that “Eric Cantor is the real power in the House of Representatives.”

(MORE: Has Nancy Pelosi Been Marginalized in the Debt Debate?)

Some Republicans argue that Obama’s praise for Boehner — and the accounts of unnamed Democratic officials who outlined Cantor’s swelling role in the debt-limit negotiations — is a gambit designed to accentuate a rift that isn’t there. “I think the White House is trying to drive a wedge between the two. That’s why Obama gave Boehner a big bear hug,” says an aide to a conservative House Republican freshman. “Both Boehner and Cantor realize a tax hike is not going to fly with the House GOP. And neither one believes that taxes are the solution.” Adds the aide, “I don’t know if just spending cuts will seal the deal.”

Monday’s negotiating session, at which the participants sought to identify common ground, provided a snapshot of Cantor’s determination not to compromise Republican principles. After Obama implored Republicans to bring ideas to the table, “Cantor came in with a specific proposal that included cuts to Medicare without providing a dime in savings through closing special-interest giveaways,” says the senior Democratic aide, who adds that Obama responded by insisting on “shared sacrifice.” Earlier in the day, Cantor told reporters that he considered “shared sacrifice” a euphemism for tax hikes. “Republicans can’t add stuff that only they want to do. That won’t pass the House or Senate,” says another senior Democratic aide briefed on the talks. “So Republicans have to start thinking about things they don’t want to do, in addition to the things Democrats don’t want to do — which means they need to start talking about revenues.”

It’s not hard to see why the rank and file in a restive Republican conference are drawn to Cantor’s hard-line haggling. During his off-camera briefing with reporters, Cantor stressed his aversion to a tax hike at every turn, insisting that any deal has “got to be net revenue neutral.” He suggested, improbably, that the most fruitful path to a deal was the framework crafted by the Biden-led group that he walked away from just weeks ago, citing irreconcilable differences over taxes. Asked how Republicans were prepared to compromise in pursuit of a deal, Cantor said the GOP was swallowing as much as it could handle by voting to raise the debt limit, an “existential question” that deeply troubles fiscal conservatives. “I don’t think the White House understands how difficult it is for fiscal conservatives to vote for a debt-ceiling increase,” he said.

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It hasn’t always been so difficult. Cantor did so on multiple occasions during the George W. Bush presidency, raising the debt limit by trillions of dollars without enacting spending cuts in the process. Now Cantor claims a vote to forestall fiscal calamity amounts to a major concession. This kind of outlook is one reason Obama remains eager to deal with Boehner, even if the GOP’s power center may be shifting.

— With reporting by Jay Newton-Small

Alex Altman is a Washington correspondent for TIME. Find him on Twitter at @aaltman82. You can also continue the discussion on TIME‘s Facebook page and on Twitter at @TIME.