WASHINGTON — President Obama began what may be his final push to win enactment of a health care overhaul, laying out a legislative blueprint on Monday that seeks to unify House and Senate Democrats but makes no big new concessions to Republicans.

Mr. Obama’s plan, which the White House said would cost $950 billion over a decade, sticks largely to the version passed by the Senate in December but addresses some of the main concerns of House leaders who are demanding more help for the middle class.

Mr. Obama’s proposal — the first time the president has provided a detailed road map for what he wants a health overhaul to look like — is the opening act to a week of high drama that will culminate on Thursday, when the president convenes Democrats and Republicans at an all-day televised health care “summit” at Blair House. The White House is hoping the session can jump start the stalled health bill.

“We view this as the opening bid for the health meeting,” Dan Pfeiffer, Mr. Obama’s communications director, told reporters Monday morning, adding, “We took our best shot at bridging the differences.”

But among Republicans leaders, the initial reaction was negative. Representative John A. Boehner of Ohio, the House minority leader, said that Mr. Obama had “crippled the credibility” of Thursday’s meeting by proposing “the same massive government takeover of health care.”

Even Democrats took a wait-and-see attitude; House leaders did not immediately embrace the plan but instead scheduled a caucus meeting for Monday. And the Congressional math is daunting for the administration. Mr. Obama has lost the 60-vote supermajority that allowed him to win passage of a bill in the Senate, which means he would either have to attract Republican support or push the bill through with a simple majority using the complex parliamentary maneuver known as reconciliation — a route that the White House pointedly did not rule out on Monday.

In the House, he needs 217 votes (the number is ordinarily 218, but two seats are vacant) — a number that could be difficult to muster, especially because Mr. Obama’s bill does not include the tighter restrictions on funding for abortion favored by abortion opponents among House Democrats.

The bill is intended to achieve Mr. Obama’s broad goals of expanding coverage to the uninsured while driving down health premiums and imposing what the White House calls “common sense rules of the road” for insurers, including ending the unpopular practice of discriminating against people with pre-existing conditions. It would offer more money to help cash-strapped states pay for Medicaid over a four-year period, and, in a nod to concerns among the elderly, end the unpopular “donut hole” in the Medicare prescription drug program.

The measure is posted on the White House Web site.

The White House projects that the bill would extend coverage to 31 million people who are currently uninsured, at a cost over 10 years of $950 billion — more than the $871 billion the Senate would have spent, but less than the $1.05 trillion for the version passed by the House. The administration estimates that its plan would reduce the federal deficit by $100 billion over the next 10 years — and about $1 trillion over the second decade — by cutting spending and reining in waste and fraud.

But the measure has not yet been evaluated by the non-partisan Congressional Budget Office, and White House officials said they were open to adjusting it if it cost substantially more than they have estimated.

In many respects, Mr. Obama’s measure looks much like the version the Senate passed on Christmas Eve — and indeed, senior White House officials acknowledged on a morning conference call that they had used the Senate bill as a template. But there are several critical differences that appear designed to appeal to House Democrats, who have voiced deep concerns about the Senate measure and its effects on the middle class.

To begin with, Mr. Obama would eliminate a controversial special deal for Nebraska — widely derided by Republicans as the “cornhusker kickback” — that called for the federal government to pay the full cost of a Medicaid expansion for that state. Instead, the White House would help all states absorb the cost of the Medicaid expansion from 2014, when it begins, until 2017.

And while the president adopts the Senate’s proposed excise tax on high-cost, employer sponsored insurance plans, Mr. Obama makes some crucial adjustments based on an agreement reached in January with organized labor leaders, while also trying to avoid the appearance of special treatment for unions. Most crucially, the president would delay imposing the tax until 2018 for all policies, not just for health benefits provided through collectively-bargained union contracts.

One unanswered question is whether the White House will attempt to push the bill through Congress using reconciliation, ordinarily reserved for budget bills. The procedure enables legislation to pass on a simple majority vote, but sharply restricts a bill’s language to provisions that have a direct impact on federal spending and revenues.

Mr. Pfeiffer suggested that is the route the White House would take in the event of a Republican filibuster. “The president expects and believes the American people deserve an up or down vote on health reform,” he said, “and our proposal is designed to give ourselves maximum flexibility to insure that, if the opposition decides to take the extraordinary step of filibustering health reform.”

In one sense, the release of the bill marks an extraordinary reversal for a president who has long said he would leave legislating to the legislators. Mr. Obama made clear from the outset of the health care debate that he would not follow the footsteps of the last Democratic president, Bill Clinton, who presented Congress with a sweeping health care proposal — only to see it fall flat on Capitol Hill.

Instead, Mr. Obama left it to Congress to produce its own measure. But after months of work, the House and Senate have been unable to close the gap between their bills. So the president, who had promised to post a Democratic measure on the Internet 72 hours in advance of Thursday’s health care meeting, was forced to take matters into his own hands.

Like the Senate version, Mr. Obama’s bill does not include a so-called public option, a government-backed insurance plan to compete with the private sector.

And the bill offers the Senate’s less restrictive language on abortion; it does not include the so-called “Stupak amendment,” which would bar insurers from offering abortion coverage to anyone buying a policy with a federal subsidy. The absence of the Stupak provision, named for Representative Bart Stupak, the conservative Michigan Democrat, could complicate matters for Mr. Obama in the House, where conservatives, led by Mr. Stupak, are adamant that the provision be included.

Mr. Obama largely adopted the Senate’s approach to paying for the legislation, including a proposed increase in the Medicare payroll tax for individuals earning more than $200,000 a year and for couples earning more than $250,000.

He opted for the Senate’s proposal to create state-based insurance exchanges, or marketplaces, rather than a single national exchange as proposed by the House. Many House Democrats worry that state exchanges would create uneven results by allowing states with lax insurance regulations to continue a hands-off approach.

And Mr. Obama adopted the Senate’s proposal to set a uniform eligibility threshold for Medicaid at 133 percent of the federal poverty level. The House had proposed setting eligibility at 150 percent of the poverty level.

House Democratic leaders, including Speaker Nancy Pelosi, had expressed serious concerns that, under the Senate bill, the subsidies provided to help moderate-income Americans afford private insurance would not be sufficient to make coverage affordable.

The Senate had provided somewhat less generous subsidies than the House for individuals and families earning below 300 percent of the federal poverty level or roughly $66,150 for a family of four, while the House bill had been less generous to those earning between $66,150 and $88,200.

Mr. Obama generally favored the Senate’s approach, but made a stab at compromise by proposing larger federal subsidies than the Senate bill did for Americans in two income categories — those earning between 133 percent and 200 percent of the poverty level, or roughly $33, 075 to $44,100 for a family of four, and those earning between 300 and 400 percent of the poverty level, or $66,150 to $88,200 for a family of four.

Still, some rank-and-file lawmakers are likely to raise concerns that working-class families will still find it difficult to afford health benefits.

Under the president’s plan, a family earning about $88,000 a year would pay no more than 9.5 percent of income toward annual health insurance premiums, or about $8,380, not including out-of-pocket costs, such as co-payments or deductibles.

Under the Senate bill, such a family could have paid $8,643 a year in premiums and under the House bill as much as $10,584 a year.

Under the president’s plan, a family earning $22,050 would have to pay $441 in annual premium costs compared to $331 under the House bill. And a family earning $33,100 would have to pay up to $1,324 a year in premiums under Mr. Obama’s plan, compared to a maximum of $993 under the House bill.