President Obama is seeking an Aug. 1 deadline for overhauling the tax code and making changes to expensive federal health programs, the final pieces of what the administration conceives as a far-reaching plan to rein in the national debt, senior administration officials said Friday.

The proposed deadline was included in a plan Treasury Secretary Timothy F. Geithner delivered to Capitol Hill on Thursday as Obama’s opening bid in talks with congressional Republicans to avert the year-end “fiscal cliff.”

That plan generally mirrors previous deficit-reduction plans Obama has submitted to Congress. In all, it would reduce borrowing over the next decade by $4.5 trillion, officials said. However, Obama is proposing to dedicate about $200 billion of those savings to new measures to boost the sluggish economy, including additional unemployment benefits and extension of a temporary payroll tax cut for most workers.

The overall figure includes about $1.2 trillion in savings already in force as part of previous spending agreements with the Republican House. The White House proposes to raise $1.6 trillion in fresh revenue, with about $1 trillion coming in January, with the expiration of the George W. Bush tax cuts for high earners.

An additional $600 billion in revenue would be generated next year through a rewrite of the tax code. And $600 billion in fresh savings would come next year, with a little more than half coming from Medicare and Medicaid changes, such as higher premiums for high-income beneficiaries.

To ensure that Congress acts by Aug. 1, Obama is proposing to delay automatic spending cuts only through that date. The so-called sequester would then act as a new trigger to force congressional action. Delaying the sequester for eight months would cost about $80 billion, officials said. They recommended covering that cost with new spending cuts and tax hikes, but did not specify which ones.

Taken as a whole, the president’s offer contains  $2.50 in spending cuts for every  $1 in new taxes, officials said. However, revenue far outweighs spending cuts in new savings, with $1.6 trillion in taxes paired with a little more than $600 billion in cuts.  

Still, the ratio is slightly better than what was described by senior Republican aides, who offered details of the plan after Geithner’s meeting with GOP leaders Thursday. At that time, GOP aides said the president had offered only $400 billion in spending cuts.  

House Speaker John A. Boehner said earlier Friday that the negotiations over the fiscal cliff had reached a “stalemate” after Obama accused Republicans of holding the middle class “hostage” and declared that tax rates must rise for the wealthy as part of any deal.

Following up on his pledge to bring his case to the American people, Obama traveled to a toy factory in Hatfield, Pa., to insist that Republicans must agree to freeze taxes for the middle class while allowing tax rates on the wealthy to increase. Republicans have insisted that although they will agree to raise taxes, they will not increase rates.

“It’s not acceptable to me, and I don’t think it’s acceptable to you, for just a handful of Republicans in Congress to hold middle-class tax cuts hostage simply because they don’t want tax rates on upper-income folks to go up,” Obama said.

During a news conference immediately after Obama’s speech, Boehner (R-Ohio) declared the fiscal cliff negotiations paralyzed. “Let’s not kid ourselves,” he said. “Right now, we’re almost nowhere.”

Boehner said that the White House’s opening bid in the talks is “not serious.”

“The president’s tax increase would be another crippling blow” for small businesses, the House speaker said, “while doing little to nothing to solve the bigger problem” of debt.

The rhetoric intensified with only weeks to go before the automatic series of deep spending cuts and tax hikes on nearly all Americans kick in. Economists say that if the fiscal cliff is not averted, the country would most likely fall into recession.

Saying he was happy to be back out in the country for the first time since his reelection, Obama once again claimed a mandate from voters on his approach to taxes and encouraged people in Pennsylvania and across the country to pressure lawmakers in coming weeks to come to a agreement.

“This was a central question in the election, maybe the central question in the election,” Obama said, speaking at the Rodon Group, a manufacturing firm that makes toys based on Nintendo and Angry Birds products, among others.

The president’s strategy reflects an evolution from his approach during his first term, when many of the budget and deficit negotiations happened behind close doors. During those days, White House officials said they struggled with compromising their ability to sell their views to the public while holding confidential talks.

The president is taking a different route this time, which includes a more muscular approach to private negotiations. On Thursday, Obama’s opening proposal called for more taxes, increased spending and an effective end to congressional control over the size of the national debt.

The proposal mirrors previous White House deficit-reduction plans and satisfies Democrats’ demands that the negotiations begin on terms dictated by president. But the offer lacked any concessions to Republicans.

Responding for the first time Friday, Boehner said he was disappointed that there had not been further progress from the White House to outline spending cuts that Obama is willing to put forward to avert the coming crisis.

“This debt doesn’t exist because we do not tax small businesses enough,” Boehner said. “It exists because Washington continues to spend too much.”

On taxes, Republicans have been arguing that the country could raise as much revenue from limiting deductions as through raising tax rates.

The White House points to independent research showing that raising rates on the wealthy would have relatively little impact on the economy and says it’s impossible to raise enough tax revenue by limiting deductions to stabilize the nation’s borrowing — and to do it without compromising the charitable deduction and other deductions.

Obama has opened the door to trimming the higher tax rates on the wealthy from what they would be if no deal were made — when the top tax brackets will go from 33 percent to 35 percent and 35 percent to 39.6 percent. Taxpayers would pay this higher rate on income earned over $200,000 for an individual, or $250,000 for a household.

Senate Minority Leader Mitch McConnell (R-Ky.) called the proposal a “step backward” from compromise — with time running out for policymakers to agree on a plan to prevent more than $500 billion in tax increases and spending cuts that could rattle the economy.

“This is a real problem. Every day, the delay brings us one step closer to the fiscal cliff that we simply must avoid,” McConnell said.

Democratic leaders, meanwhile, were triumphant after ­receiving similar briefings from Geithner and White House legislative affairs director Rob Nabors. Top Democrats have insisted for months that an Obama victory would entitle them to demand far more in new taxes than Republicans have been willing to consider, to seek new measures to boost economic growth, and to avoid major cuts to entitlement programs such as Social Security and Medicare.

“Democrats are on the same page,” said Senate Majority Leader Harry M. Reid (D-Nev.). “The president has made his proposal; we need a proposal from them.”

Although the White House offer seemed to startle Republicans, it contains little that would be unfamiliar to anyone following the president’s recent public statements. The exception was his proposal on the federal debt limit. GOP aides said Obama is seeking to permanently enact procedures that were temporarily adopted in the summer of 2011 that allow the White House to unilaterally increase the debt ceiling unless two-thirds of lawmakers disapprove.

That process, initially proposed by McConnell, was not intended to become permanent. By trying to make it so, Obama is seeking to avoid another damaging battle over the debt ceiling that would again risk a national default. This change, however, would also deprive Congress of its historic authority over federal borrowing.

Unless Congress acts on the fiscal cliff, taxes will rise significantly in January for nearly 90 percent of Americans, and about $65 billion will be sliced from the budgets of the Pentagon and other agencies, probably triggering a recession. Simply canceling the changes, however, risks undermining confidence in the nation’s ability to manage its rising debt.

Obama’s offer comes nearly two weeks after Boehner and other congressional leaders opened talks at the White House. Since then, administration officials have negotiated directly with Boehner’s staff. Senior Republican aides said relations deteriorated in recent days, prompting Boehner to call the White House on Wednesday evening to request to speak with the president.

Boehner’s aides declined to comment on the 28-minute call, but Republicans in the Capitol said Obama dominated the conversation and was forceful in demanding that Boehner pass legislation to maintain tax rates for the middle class and let them rise on income over $250,000 a year.

Boehner called the discussion “frank and direct” and said he remains “hopeful that productive conversations can be had in the days ahead.” Both sides confirmed that no additional meetings have been planned, but emphasized that talks will continue.

Obama’s proposal, as outlined by Republicans, would purportedly trim the debt by about $4 trillion over the next decade, in part through spending cuts already in force and savings from ending the wars in Iraq and Afghanistan.

With regard to taxes, the White House wants about $1 trillion in new revenue from the year-end expiration of the George W. Bush-era tax cuts on income over $250,000. Obama also is demanding that dividends be taxed as normal income and that the estate tax be raised to 45 percent and expanded to cover estates worth as little as $3.5 million — policies for which the Democratic Senate was unable to win approval this year.

The rest of the tax increases and the entitlement savings would come next year, through congressional revisions to the tax code and retirement programs.

The White House proposal would delay automatic cuts at federal agencies for one year while funding other Democratic priorities, including $50 billion for a new infrastructure bank and additional benefits for unemployed workers.

The plan also calls for extending the payroll tax cut, or adopting a similar tax break for working families, in addition to extending income tax cuts for the vast majority of taxpayers.

“Right now, the only thing preventing us from reaching a deal that averts the fiscal cliff and avoids a tax hike on 98 percent of Americans is the refusal of congressional Republicans to ask the very wealthiest individuals to pay higher tax rates,” White House spokeswoman Amy Brundage said. “We remain willing to do tough things to compromise, and it’s time for Republicans in Washington to join the chorus of other voices . . . who support a balanced approach that asks more from the wealthiest Americans.”

Staff writer Paul Kane contributed to this report.