The debate over the overhaul of the nation's health-care system got off to a rocky start in the Senate on Wednesday as lawmakers delayed action on one key bill.

WASHINGTON — The debate over the overhaul of the nation’s health-care system got off to a rocky start in the Senate on Wednesday as lawmakers delayed action on one key bill.

Senate leaders said they were on track to put a bill on the floor by midsummer, but some Democrats privately said that piecing together a measure is proving excruciatingly difficult, particularly if the goal is to pass a bill with Republican support.

“A bipartisan bill takes far more time than not,” said Sen. Max Baucus, D-Mont., chairman of the Senate Finance Committee, which had been expected to unveil a package of changes by Friday and hold a committee vote next week.

Amid concerns from Republicans and some Democrats about the cost, Baucus said he has agreed “to slow things down” and committee action could be delayed until after the July 4 recess.

The complex legislation attempts to slow increases in health-care costs, thus freeing up money to cover the nearly 50 million uninsured.

The Finance Committee package is eagerly awaited because lawmakers, lobbyists and overhaul advocates believe that panel has the best chance of producing a measure that can win broad support.

Baucus is working with Sen. Charles Grassley, R-Iowa, and other Republicans on the panel to hammer out a plan, along with a proposal to pay for it.

That effort hit a snag this week when the Congressional Budget Office attached a $1.6 trillion price tag to a preliminary version, far more than many senators are prepared to spend.

The figure shocked key Democrats, who were scrambling Wednesday to make adjustments that would slash the price by more than a third.

Among the changes under discussion, according to Sen. Kent Conrad, D-N.D.: tightening eligibility for federal subsidies to purchase insurance, which had been set at 400 percent of the federal poverty level; and potentially requiring businesses to pay more if they decide not to provide coverage to their workers.

Committee members also were struggling with the shape of a government-sponsored insurance plan that would be available to people who couldn’t get covered elsewhere. Republicans are opposed to any government-run plan

The panel also had yet to settle on a financing package, though aides said they were looking at imposing a tax on the health premiums millions of families receive through their employers, with any premiums of more than $17,000 a year being taxed as income beginning in 2013.

Setting the cap that high would generate less revenue than Democrats had hoped for, a Finance Committee aide said, forcing them to revisit an idea they had once rejected: President Obama’s proposal to tax high-earning families by limiting the value of their itemized deductions.

Baucus vowed that the final bill would cost less than $1 trillion over the next decade and the committee would offer a plan to cover the entire cost.

Delicate deal making was going on behind the scenes at the White House as well, where administration officials were talking to drugmakers about voluntarily expanding prescription-drug benefits for Medicare recipients, said House Majority Leader Steny Hoyer, D-Md.

Meanwhile, the Senate Health, Education, Labor and Pensions Committee was quickly mired in acrimony as it opened debate on a different plan representing the hopes of liberal Democrats.

Separately, two new health-care plans were introduced Wednesday. House Republicans introduced a proposal that would provide tax credits to help the uninsured buy coverage from private insurers.

And three former Senate leaders unveiled a $1.2 trillion plan, fully paid for, that would cover the uninsured. The plan by Democrat Tom Daschle and Republicans Howard Baker and Bob Dole would tax some health-care benefits as if they were income.

Material from The Associated Press is included in this report.