President Obama’s campaign to overhaul the nation’s healthcare system is officially on the back burner as Democrats turn to the task of stimulating job growth, but behind the scenes party leaders have nearly settled on a strategy to salvage the massive legislation.

They are meeting almost daily to plot legislative moves while gently persuading skittish rank-and-file lawmakers to back a sweeping bill.

This effort is deliberately being undertaken quietly as Democrats work to focus attention on more-popular initiatives to bring down unemployment, which the president said was a priority in his State of the Union address on Wednesday.

Many have concluded that the only hope for resuscitating the healthcare legislation is to push the issue off the front page and give lawmakers time to work out a new compromise and shift public perception of the bill.

“A little bit of time and quiet could help,” said Arkansas Sen. Mark Pryor, a conservative Democrat who was among a group of centrist Democrats from the House and Senate who met last week to discuss a way forward on healthcare.

“Human nature being what it is, it’s always easier to be against something than to be for it. And if you create any uncertainty with change, opponents can jump on that and just try to scare people. . . . That has been hard to overcome politically,” Pryor said. “Maybe over time, people will have a chance to understand what is in the legislation.”

House Speaker Nancy Pelosi (D-San Francisco) and Senate Majority Leader Harry Reid (D-Nev.) particularly want to give members time to recover from the shock of Republican Scott Brown’s victory in the Massachusetts Senate race two weeks ago. The election cost Democrats their filibuster-proof Senate majority.

But in the coming weeks, Pelosi and Reid hope to rally House Democrats behind the healthcare bill passed by the Senate while simultaneously trying persuade Senate Democrats to approve a series of changes to the legislation using budget procedures that bar filibusters.

At the same time, leading consumer groups, doctors and labor unions that have backed the healthcare legislative effort for more than a year are stepping up attempts to stiffen lawmakers’ resolve.

Almost all of the proponents of a healthcare overhaul are desperate to avoid a repeat of the contentious public debate and deal-making that consumed Capitol Hill last year.

“In a 24-hour news cycle, with the Internet and bloggers and cable news, sometimes a lot more can be accomplished, especially with healthcare, when it happens behind closed doors,” said Drew Altman, a healthcare policy expert who heads the nonprofit Henry J. Kaiser Family Foundation.

Democrats, who would almost certainly get no Republican votes for their bill, still must overcome substantial obstacles.

Many rank-and-file Democrats remain rattled by Brown’s winning campaign in Massachusetts, which in part targeted the healthcare bill in Washington. Recent national polls indicate that fewer than 40% of Americans like the healthcare legislation being pushed by Obama and his congressional allies.

Some Democrats would prefer to vote on a series of more limited bills targeting pieces of the healthcare system, an approach that House leaders are exploring. A group of liberal House lawmakers are pushing for inclusion of a new government insurance plan, or public option, in the final bill.

Tensions also remain high between Democrats in the House and Senate. Many House lawmakers blame the Senate bill for fueling public opposition with provisions such as a new tax on high-end “Cadillac” health plans and special aid for Nebraska that was added at the 11th hour to satisfy the state’s Democratic senator.

At a closed-door caucus meeting last week, Rep. Edward J. Markey (D-Mass.) won applause from his colleagues when he told a story about being confronted recently by an angry voter in his district who said he didn’t want his health benefits taxed to pay off Nebraska.

Democrats hope to use a process known as budget reconciliation, which allows budget-related legislation to be passed with a simple majority in the Senate rather than the 60-vote majority that has become necessary given the threat of Republican filibuster.

But many House Democrats do not want to vote on the Senate bill until the Senate passes the fixes they want.

And it is unclear whether the Senate could approve a package of changes to its bill before the House approves the underlying legislation, according to senior Democratic aides. Democratic leaders hope to agree on a procedural path forward by the end of this week.

Despite the hurdles, there is a growing consensus that a modified Senate bill may offer the best hope for enacting a healthcare overhaul.

“The more they think about it, the more they can appreciate that it may be a viable . . . vehicle for getting healthcare reform done,” said Rep. Gerald E. Connolly (D-Va.), president of the Democratic freshman class in the House.

Sen. Tom Harkin (D-Iowa), who chairs the Senate health committee, noted that even before the Massachusetts election, senior Democrats had substantially agreed on a series of compromises that addressed differences between the House and Senate healthcare bills.

These included scaling back the Cadillac tax, boosting aid to help low- and moderate-income Americans buy insurance, closing the “doughnut hole” in the Medicare prescription drug plan, and giving all states the assistance that Nebraska secured to expand Medicaid.

noam.levey@latimes.com