WASHINGTON  — A House committee plowed ahead today on a health care overhaul bill, with the clock running on chances for progress on President Barack Obama's top domestic priority before Congress takes its August break.

As Chairman Henry Waxman, D-Calif., restarted the Energy and Commerce Committee's voting session, he warned lawmakers against offering amendments that make the bill more expensive — and agreed to a Republican suggestion to limit the time allowed for debate. Waxman said he hopes to finish the bill sometime Friday.

Meanwhile, a small group of Senate negotiators pursued an elusive bipartisan deal. Finance Committee Chairman Max Baucus, D-Mont., and his Republican counterpart, Sen. Charles Grassley of Iowa, had both indicated Wednesday the group of six senators was making progress. But prospects for a Finance Committee breakthrough remained uncertain.

The progress in the House came after Democratic leaders won agreement from conservative Democrats on the Energy and Commerce Committee to allow the panel to proceed. It would be the last of three House committees to finish work, clearing the way for a floor vote in September.

The Finance panel and the Energy and Commerce panel are seen as pivotal tests of prospects for the legislation because they reflect the broader composition of the Senate and the House.

The two House committees and one Senate panel that have already passed versions of the legislation are dominated by Democratic liberals.

One liberal, Sen. Tom Harkin, D-Iowa, said today the obstacles to the bill mean that Congress probably can't finish its work until late fall. "The president wanted to have it on his desk in October," said Harkin. "Well, he'll probably have it in November now. But I'm very hopeful we'll get it done at least by that time."

The House bill and the plan under negotiation in the Senate are designed to meet Obama's goals of spreading health coverage to millions who now lack it, while trying to slow the skyrocketing growth in medical costs. As recently as two weeks ago, Obama was pressing the House and Senate to pass separate bills by the end of July or early August. After Republicans and moderate Democrats objected to the rush, the president said he'd settle for just progress.

Wednesday in the House, Democratic leaders gave in — at least temporarily — to numerous demands from rank-and-file rebels from the conservative wing of the party. The so-called Blue Dog Democrats had been blocking the bill's passage in Energy and Commerce.

The House changes, which drew immediate opposition from liberal lawmakers, would steer away from using Medicare as the blueprint for a proposed government insurance option, reduce federal subsidies to help lower-income families afford coverage, and exempt additional businesses from a requirement to offer health insurance to their workers.

Bipartisan Senate negotiators reported progress on legislation that aims to cover 95 percent of Americans without raising federal deficits.

Finance chairman Baucus said preliminary estimates from congressional budget experts showed the cost of the emerging Senate plan was below $900 billion and would result in an increase in employer-sponsored insurance — conclusions that may reassure critics who fear a bloated bill that prompts businesses to abandon the coverage they currently provide.

Congressional officials said Baucus was able to get the cost under $1 trillion because his bill includes only the cost of the first year of a 10-year, $245 billion program to increase doctor fees under Medicare. House Democrats used a similar sleight of hand, excluding the entire $245 billion when claiming their measure wouldn't add to the deficit.

The White House praised the developments in the House. At appearances in North Carolina and Virginia, the president sought to minimize the significance of the slippage in his timetable.

Rep. Mike Ross of Arkansas, a leader of the Blue Dogs, said the changes agreed to by the leadership in the House bill would cut its cost by about $100 billion over 10 years. But his claim has been called into question.

A new break for small businesses, among other changes in the deal, also increased costs substantially, so it wasn't clear that the agreement actually generated net savings.

Waxman said the cost of helping small businesses was offset by a reduction in the level of federal subsidies that would be available to help people buy health insurance. The net result appeared to be a wash.

The House deal was worked out over hours of talks that involved not only Democratic leaders but also White House officials eager to advance the bill. Senior congressional aides cast it as a temporary accommodation, saying leaders had not committed to support it once the bill advances to the floor of the House in the fall.

As word of the agreement spread, liberals fired back. "We do not support this," said Rep. Lynn Woolsey, D-Calif., co-chair of the Progressive Caucus. "I think they have no idea how many people are against this. They can't possibly be taking us seriously if they're going to bring this forward."

— Associated Press writers Liz Sidoti, Alan Fram and David Espo contributed to this report.