WASHINGTON — Democrats on Thursday unveiled the completed version of the health care legislation they intend to bring to a vote this weekend, saying that it would more than pay for itself over the next decade while extending insurance coverage to most of those who lack it.

With his party scrambling to line up the last commitments it needs to push the legislation through Congress, the White House announced that President Obama had canceled a trip abroad that had been scheduled to begin Sunday, the same day the House is likely to hold its most important vote on the bill.

House Democrats said the prospects for passage were improved by the assessment of the completed legislation that was released Thursday by the nonpartisan Congressional Budget Office. The office found that that the bill would reduce federal budget deficits by $138 billion over the next 10 years.

The No. 3 Democrat in the House, Representative James E. Clyburn of South Carolina, said “we are absolutely giddy” over the estimate.

He and his colleagues immediately started using the report to try to persuade fiscally conservative Democrats that the bill would not lead to a huge increase in the deficit and federal debt, as Republicans contend.

Democrats see no prospect of obtaining any Republican votes for the bill. But on Thursday the Democrats locked in the support of two members of their own party once considered doubtful: Representatives Bart Gordon of Tennessee, who had originally opposed the measure, and Luis Gutierrez of Illinois, who had been wavering over immigration language in the bill.

The measure, a top priority for Mr. Obama and Nancy Pelosi, the Speaker of the House, would be the biggest change in social policy in decades.

“Passage of health care reform is of paramount importance, and the president is determined to see this battle through,” Robert Gibbs, the White House press secretary, told reporters as he announced the postponement of Mr. Obama’s trip to Indonesia. Australia and Guam. The trip will be made in June instead, he said.

Under the bill, the budget office said, the federal government would spend $940 billion over the next 10 years to provide coverage to 32 million people who would otherwise be uninsured.

The price tag, though higher than the $875 billion estimated cost for the Senate’s version, still comes in under the $950 billion limit suggested by Mr. Obama, who has said he would not sign a bill that added a dime to the deficit.

The cost of the bill results from a significant expansion of Medicaid, to cover 16 million more low-income people, and from federal subsidies to help moderate-income people buy health insurance on their own.

House Democrats said that they had reduced the impact of a proposed tax on high-cost employer-sponsored health plans. White House officials have described the tax as a way to slow the growth of health spending, but labor unions dislike it.

Under the Senate bill, the tax would have raised $149 billion over 10 years. The new legislation delays and reduces the tax, slashing expected revenues to $32 billion.

Democrats would make up for some of the lost revenue by increasing the Medicare payroll tax and by extending it to capital gains, dividends, interest and other “unearned income” of people with adjusted gross incomes over $250,000 for married couples and $200,000 for individuals.

House Democrats plan to approve the bill passed by the Senate in December. And they intend to approve a package of changes, using a procedure known as budget reconciliation, to avoid the threat of a Republican filibuster in the Senate. Under this plan, the president would sign the first bill into law, and the second bill would go to the Senate, where it can be approved by a simple majority vote. Republicans will try to block it or alter it by offering dozens of amendments and points of order, but will not be able to filibuster it.

Ms. Pelosi is ready for a fierce fight. Republicans and insurance companies “will do anything to stop this legislation,” she said.

The Senate Republican leader, Mitch McConnell of Kentucky, said the new legislation was “worse than the Senate bill.”

Republicans said the budget office’s cost estimates should not provide any comfort to people who are worried about the federal deficit. They say the picture in the first decade is too rosy because many of the taxes and fees would start immediately, while the major costs of the bill would not appear for four years. In addition, they said, the projected Medicare savings may be unrealistic and unsustainable, because they would reduce payments below the costs incurred by many hospitals. And the bill would not prevent cuts in Medicare payments to doctors that are scheduled to occur under existing law.

Finally, Republicans said that the anticipated reduction in the deficit, $138 billion over 10 years, is dwarfed by the $652 billion deficit reported by the government for just the last five months.

The budget office said the Democrats’ bill would probably reduce deficits beyond 2019, although it acknowledged a high degree of uncertainty about such estimates. Democrats said the savings would total $1.2 trillion in the decade starting in 2020.

The bill would significantly increase penalties for employers who do not offer health coverage. If an employer with more than 50 workers does not offer coverage, and if any of its workers obtains subsidized coverage through an exchange, the company would have to pay a penalty — a tax — of $2,000 for each full-time employee; the penalty under the Senate bill would have been $750 per employee.

The new bill would also make deeper cuts than the Senate bill in payments to private Medicare Advantage plans.