The drive for a major deficit-reduction deal entered a new phase Thursday when Republican negotiators pulled out of bipartisan talks, leaving it to President Barack Obama and House Speaker John Boehner to resolve the toughest issues.

House Majority Leader Eric Cantor (R., Va.) said he was backing out of the talks for now because the group had reached an impasse over the question of whether tax increases should be included in the deal.

The only other Republican in the group, Sen. Jon Kyl (R., Ariz.), soon followed suit, agreeing that only the highest levels of leadership could break the logjam between Democrats' demand that the budget deal include tax increases and Republicans' adamant opposition to that demand.

The talks were aimed at striking a budget deal in hopes of easing the way for Congress to raise the government's $14.29 trillion debt limit. Treasury Department officials say that without additional borrowing authority, the government will run out of cash to pay its bills by Aug. 2. They warn that defaulting on any U.S. obligations could trigger another financial crisis and recession.

The group, led by Vice President Joseph Biden, canceled its scheduled meeting Thursday. The suspension of the group's work could mark the beginning of the final stage of budget negotiations, which most participants had long assumed would be concluded by the president, the speaker and Senate Majority Leader Harry Reid (D., Nev.)