Washington (CNN) -- A day after competing nationally televised speeches by President Barack Obama and House Speaker John Boehner, talks on a debt-ceiling deal to avert a government default next week generated fresh hostility Tuesday amid some signs of possible movement.

While political leaders continued sniping at each other's latest proposals, conservative Senate Republican Leader Mitch McConnell called for renewed negotiations with Obama and indicated his party must be willing to move away from some of its demands.

"We are going to have to get back together and get a solution here," McConnell said of formal talks with the White House and congressional Democrats. "We cannot get a perfect solution, from my point of view, controlling only the House of Representatives. So I am prepared to accept something less than perfect because perfect is not achievable."

Devil is in the downgrade

In addition, the latest Republican proposal unveiled Monday by Boehner, R-Ohio, appeared in danger of failing to get passed by the GOP-controlled House, which would weaken the party's negotiating leverage on a final deal.

A vote had been expected on Wednesday, but the plan ran into major trouble Tuesday when the Congressional Budget Office said it failed to reduce spending and deficits as much as advertised. A spokesman for Boehner said aides are looking at rewriting the plan, and a congressional source told CNN on condition of not being identified that the vote was being postponed until Thursday at the earliest.

Conservatives including some House and Senate Republicans and the Club for Growth, an anti-tax group, have criticized the Boehner plan for not doing enough to tackle the nation's mounting deficits and debt.

"I'm not voting against the speaker, but I'm voting against this plan," Rep. Jim Jordan, a fellow Ohioan who heads the conservative Republican Study Committee, told CNN. Asked if Boehner had the votes to pass the measure in the chamber he leads, Jordan said: "I don't think so now."

Boehner backed into a corner

In a letter to their House colleagues, a group of conservative senators harshly criticized the Boehner plan as insufficient and called on Republicans to reject it in favor of the "cut, cap and balance" plan previously passed by the House and dismissed by the Senate.

"For many reasons, we cannot support this bill and urge you to protect the American taxpayers by strongly opposing this bill," said the letter from Republican Sens. Jim DeMint of South Carolina, Rand Paul of Kentucky, Mike Lee of Utah and David Vitter of Louisiana.

Meanwhile, Capitol Hill phone lines were jammed and websites of key lawmakers -- including House Speaker John Boehner -- crashed as citizens from coast to coast tried to weigh in on the debate following Obama's call Monday night for the public to push their elected representatives to reach a deal.

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The number of phone calls to House offices was about 35,000 an hour, well above the normal average of 20,000 an hour but well below the 50,000 an hour rate at the height of the health care debate, said Salley Wood of the House Administration Committee.

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.

Some financial analysts have warned of a potential stock market crash and a downgrade of America's triple-A credit rating.

Officials also warn that without an increase in the debt limit, the federal government would not be able to pay all its bills next month. Obama recently indicated he could not guarantee that Social Security checks would be mailed out on time.

Leaders from both parties have put forward plans tying a debt-ceiling increase to future spending reductions. Publicly, however, neither Democratic nor Republican leaders have indicated a willingness to consider the latest proposals put forward by their counterparts.

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Senate Majority Leader Harry Reid, D-Nevada, said Tuesday that the proposal by Boehner is a market-rattling "short-term solution" that would be "dead on arrival in the Senate, if it gets out of the House." Boehner called Reid's blueprint a "blank check" for more uncontrolled spending that would undermine the economy.

House Minority Leader Nancy Pelosi, D-California, accused Republicans of trying to "undermine government" and "destroy" vital programs; McConnell, R-Kentucky, insisted Obama is "clinging" to hope for a "massive tax hike."

The latest rhetorical volleys came little more than 12 hours after Obama's nationally televised plea for compromise.

"This is no way to run the greatest country on Earth," Obama said Monday night. "The American people may have voted for divided government, but they didn't vote for a dysfunctional government."

The president also jumped into the partisan fray, ripping House Republicans for stubbornly pursuing a "cuts-only approach" that "doesn't ask the wealthiest Americans or biggest corporations to contribute anything at all."

Obama renewed his call for a "balanced approach" that would include no extension of Bush-era tax cuts for families making more than $250,000 a year, and encouraged Americans to let their political leaders know their desire for a compromise instead of the congressional stalemate.

Boehner, in turn, blasted Obama in a nationally televised response, accusing the president of engaging in a debilitating "spending binge" and pushing "tax increases (that) will destroy jobs."

Despite the poisonous partisan atmosphere, the Reid and Boehner plans remain the focal points of talks between the two parties.

Both plans provide a path to raise the debt ceiling through the end of 2012, but they differ in scope and in key components involving requirements for future congressional action.

Obama has endorsed Reid's plan, but he acknowledged it has little chance of getting passed in the GOP-led House. White House Press Secretary Jay Carney insisted on Tuesday that Boehner's plan will never clear the Democratic-controlled Senate.

Reid's blueprint calls for roughly $2.7 trillion in spending cuts over the next decade while raising the debt limit by $2.4 trillion -- an amount sufficient to fund the government through 2012, which means past next year's election.

It also would establish a congressional committee made up of 12 House and Senate members to consider additional options for debt reduction. The committee's proposals would be guaranteed by a Senate vote with no amendments by the end of the year.

Reid stressed Tuesday that his plan doesn't include tax hikes and would cut spending more than it increases the debt ceiling -- two key GOP demands.

"Every single spending cut in the proposal has already been endorsed by Republicans," Reid said. "It's everything the Republicans have demanded wrapped up in a bow and delivered to their door."

The only thing preventing a deal, Reid argued, are tea party-backed "right-wing ideologues" in the House.

Boehner, however, argued at a Monday afternoon news conference that Reid's plan is "full of gimmicks" and "doesn't deal with the biggest drivers of our deficits and debt, and that's entitlement programs." On Tuesday, McConnell argued that the Reid plan "is not a serious effort to address deficit and debt, and should be defeated."

Boehner's plan would require two separate votes by Congress to increase the debt ceiling -- which Obama and Democrats oppose -- in a package that was intended to include approximately $1.2 trillion in spending cuts over the next decade and setting up a special congressional committee to recommend more debt reduction measures worth another $1.6 trillion or more in savings. Any failure on the part of Congress to enact the mandated spending reductions would trigger automatic across-the-board budget cuts.

This plan is "reasonable" and "responsible," Boehner said Tuesday. "We're going to have some work to do to get it passed, and I think we're going to do it."

However, the CBO analysis indicated that Boehner's measure would bring spending cuts of $850 billion instead of the $1.2 trillion claimed, while it also would increase the debt ceiling by $900 billion. Boehner has pledged that any debt-ceiling increase would be matched by equal or greater spending reductions.

After the CBO numbers came out, Boehner said in a statement, "We promised that we will cut spending more than we increase the debt limit -- with no tax hikes -- and we will keep that promise.

"As we speak, congressional staff are looking at options to adjust the legislation to meet our pledge," Boehner's statement said.

Democrats argue that holding more than one vote to raise the debt limit through the 2012 election leaves financial markets uncertain that the same political wrangling over a deal occurring now will happen again next year.

The White House released a statement Tuesday stressing that "the administration strongly opposes" Boehner's proposal. If it reaches Obama's desk, the statement said, "the president's senior advisors would recommend that he veto this bill."

That language, while constituting a veto threat, was softer than previous documents on other issues that stated directly the president would veto the legislation involved.

Republicans want to lock in long-term tax and spending changes, and argue that Obama is trying to avoid politically tough decisions in a presidential election year.

Boehner, who is expected to win little Democratic support, pleaded with members of the House GOP caucus Tuesday morning to unify behind his proposal when it comes up for a vote as soon as Wednesday, according to two GOP sources.

"It comes down to the people in this room. It comes down to the willingness to stand together. This is the path to victory for the American people," the sources quoted Boehner as telling the meeting.

House Majority Leader Eric Cantor, R-Virginia, told the meeting he understands that "the debt limit vote sucks," and he praised Boehner's leadership, the sources said.

Cantor urged House Republicans to remain unified and call the president's bluff -- a reference to Obama's threat to veto any bill that fails to ensure a debt limit extension through the 2012 election.

As the debt-ceiling debate drags on, a new CNN/ORC International Poll reveals a growing public exasperation and demand for compromise. Sixty-four percent of respondents to a July 18-20 survey preferred a deal with a mix of spending cuts and tax increases. Only 34% preferred a debt reduction plan based solely on spending reductions.

According to the poll, the public is sharply divided along partisan lines. Democrats and independents, according to the CNN/ORC Poll, are open to a number of different approaches because they think a failure to raise the debt ceiling would cause a major crisis for the country. Republicans, however, draw the line at tax increases, and a narrow majority of them oppose raising the debt ceiling under any circumstances.

Fifty-two percent of Americans think Obama has acted responsibly in the debt-ceiling talks so far, but nearly two-thirds say the Republicans in Congress have not acted responsibly. Fifty-one percent would blame the GOP if the debt ceiling is not raised; only three in 10 would blame Obama.

CNN's Ted Barrett, Brianna Keilar, Kate Bolduan, Keating Holland, Xuan Thai and Deirdre Walsh contributed to this report.