Washington (CNN) -- House Speaker John Boehner is in a tough position: between a rock and a hard place, wedged squarely into a corner.

On one side, he has President Obama painting him as a stubborn teenager who is unwilling to meet halfway on the debt ceiling.

On the other side, he has the small but powerful tea party freshman class in the House, many of whom are unapologetic in their desire not to give an inch on tax increases and are quite willing to push the negotiations to -- and possibly over -- the edge.

Then, he has his No. 2, House Majority Leader Eric Cantor, who has been at his side through the crisis but has also been seen as the aggressive, rising leader of the new, young, conservative minority in Congress.

And then there are his constituents in Ohio and fans across the country, many of whom are flooding his office with calls of support, overwhelming the number of calls against the congressman.

"It comes down to the willingness (of Republicans) to stand together," Boehner said. "This is the path to victory for the American people."

House call center near capacity

Boehner, meanwhile, is trying to get his party through this crisis politically intact, corralling a group of House Republicans and tamping down criticism from tea party groups squarely opposed to his proposal to tackle the country's debt crisis.

His plan -- roughly $3 trillion in cuts and raises to the debt ceiling in two stages -- is being attacked from the right by Republicans who don't think it goes far enough in reforming government spending. And he has been unable to secure enough support from Democrats by sweetening the bill with enough of what they want to offset the tea party conservatives he's sure to lose.

Debt ceiling impasse: How we got into this mess

He needs 217 votes to pass the bill. According to congressional watchers, he doesn't have it.

On Tuesday, Boehner was dealt a blow when the Congressional Budget Office released figures showing that his plan would reduce deficits by only $851 billion over 10 years -- less than what he was expecting.

Boehner's office said the Ohio Republican will rewrite his debt ceiling legislation to ensure that it meets his oft-stated pledge to cut spending more than Congress increases the federal borrowing limit.

The 60 House tea party caucus members -- including many of the Republican freshmen -- have seemingly painted Boehner into a corner. Any deal, they say, must include nearly $4 trillion in spending and absolutely no tax increases, something Obama has publicly advocated.

Debt debate cheat sheet

Boehner, who had been holding intense talks with Obama, withdrew from negotiations over a "grand bargain" after finding opposition from his party. Meanwhile, Republicans in the Senate, including Minority Leader Mitch McConnell, are pushing for a short-term deal.

Many freshman congressmen sailed into office in the 2010 midterm elections on a wave of fiscal responsibility spurred on by tea party groups who opened their pockets and support. Many within the GOP even signed an Americans for Tax Reform pledge that they would say no to any new taxes.

While Boehner's debt ceiling bill, released Monday, does not include any tax increases, many within his own party are opposed because it does not include a key part of their "cut, cap and balance" plan: a requirement that Congress pass a balanced budget amendment before raising the debt ceiling. The speaker's outline mandates both chambers vote on an amendment before the end of the year but doesn't mandate that it pass.

Read more about Boehner's plan

Complicating Boehner's task is that he has little wiggle room to get his bill passed. It needs at least 217 votes, so House Republican leaders can afford to lose only 23 from their 240-seat majority. If the solid wall of Democratic opposition holds up and he is unable to convince enough of them to switch sides, it will be tough to push the bill through to the Senate.

Norm Ornstein, a resident scholar at the American Enterprise Institute for Public Policy Research, said Boehner "has a big headache inside his own caucus."

"You've got senior members like Jim Jordan of Ohio, the head of the Republican Study Committee ... which is the kind of conservative caucus about 40 years ago. It was a fringe group, a small fraction of the Republican Party. Now, it's 80%," he said.

Jordan came out against Boehner's plan, saying that although he thanks him for fighting for GOP principles, "I cannot support the plan."

Jordan and 38 other House Republicans have signed a pledge that he will not vote to raise the debt ceiling if aspects of the cut, cap and balance bill that passed the House last week aren't included in the plan. Boehner admitted that his plan is "built on the principles" of that plan but doesn't go as far as that bill would.

Chris Chocola, president of the conservative group Club for Growth, said Tuesday that his group cannot back Boehner's plan.

"The Boehner plan does not achieve the goals of cut, cap and balance and doesn't fix our fiscal mess," he said. "We are urging club members to call their members of Congress and ask them to oppose it."

The Cut, Cap and Balance Coalition, which includes more than 100 groups, argued that it understands the pressure on Boehner and congressional leaders to get a deal done before August 2 but said they should not exclude the cut, cap and balance bill.

"We applaud the speaker's commitment to avoiding tax increases on job creators as part of an increase in the debt ceiling," spokesman Joseph Brettell said in a statement Monday. "Unfortunately, the speaker's plan falls short of meeting these principles."

Brettell said that although he is not criticizing the speaker himself, the coalition "cannot support his framework, and we urge those who have signed the pledge to oppose it and hold out for a better plan."

He pointed to a provision in Boehner's plan that would create a congressional commission to tackle future deficit issues. "History has shown that such commissions, while well-intentioned, make it easier to raise taxes than to institute enduring budget reforms," he said.

If Congress fails to raise the $14.3 trillion debt limit by August 2, Americans could face rising interest rates and a declining dollar, among other problems. As the cost of borrowing rises, individual mortgages, car loans and student loans could become significantly more expensive.

While the competing GOP and Democratic plans are close on spending cuts, the issue is over Obama's plan to reform the tax system in order to raise revenue. Republicans, no doubt, are in lock step against it.

But polls indicate that Obama has the backing of the American public.

A CNN/ORC International Poll taken July 18 through 20 found that only 34% of respondents backed only spending cuts, while 64% said the budget plans must including a mix of spending cuts and tax increases.

"(Polls show) that more people right now trust President Obama than the House Republicans on both the issue of the debt and the deficit," said Ron Brownstein, CNN senior political analyst and editorial director at The National Journal.

Brownstein said that on the other hand, as those numbers suggest, people do not share the sense of urgency that the possibility of default is a crisis in the same way Wall Street and most economists do.

The CNN/ORC Poll found that only 18% said a crisis would occur if the U.S. defaulted on its loans, as several economists say would happen. In addition, 43% said there would be major problems, 31% said minor problems and 6% expected no problems.

The pressure for congressional leaders to do something to get the debt ceiling raised will then have to come from the business community, Brownstein added.

"That pressure is going to have to come from elite institutions like the U.S. Chamber of Commerce, which was a big supporter of the Republicans and is now warning that default would be 'catastrophic,' " he said.

CNN's Tom Cohen, Alan Silverleib, Shannon Travis and Deirdre Walsh contributed to this report.