WASHINGTON — Their government has failed to keep the doors open and has told federal workers to stay off the job as the political parties fight over spending and health care in austere times.

Now Congress and President Barack Obama are poised to send this message to the 800,000 sidelined government employees: We don’t know when the impasses will end but you will get reimbursed for lost pay once the government reopens.

With the partial shutdown entering its fifth day, the GOP-run House was debating a bill Saturday that would make sure the furloughed workers get paid for not working. The White House backs the bill and the Senate was expected to OK it, too, but the timing was unclear.

Several Washington-area lawmakers made impassioned pleas to provide relief for federal workers, many of whom live in their districts.

“This is not their fault and they should not suffer as a result,” said Rep. Elijah Cummings, D-Md.

Obama’s budget office assessed the plan this way: “Federal workers keep the nation safe and secure and provide vital services that support the economic security of American families. The administration appreciates that the Congress is acting promptly to move this bipartisan legislation and looks forward to the bill’s swift passage.”

The White House has opposed other piecemeal efforts by House Republicans to restore money to some functions of government during the partial shutdown. White House officials have said the House should reopen the entire government and not pick agencies and programs over others.

In the 1995-96 government shutdowns, furloughed workers were retroactively given full pay.

Despite the White House’s declared appreciation of the essential the role of federal workers, there appeared no sign of a breakthrough in getting them back to work.

Lawmakers keep replaying the same script on Capitol Hill: House Republicans pass piecemeal bills to reopen popular and politically sensitive programs — on Friday, disaster relief and food aid for the poor — while Democrats insist that the House vote on a straightforward Senate-passed measure to reopen all of government.

“But the far right of the Republican Party won’t let Speaker John Boehner give that bill a yes-or-no vote,” Obama said in his Saturday radio and Internet address. “Take that vote. Stop this farce. End this shutdown now.”

There seemed little chance of that.

For one thing, flinching by either side on the shutdown might be seen as weakening one’s hand in an even more important fight looming just over the horizon as the combatants in Washington increasingly shifted their focus to a midmonth deadline for averting a first-ever default.

“This isn’t some damn game,” Boehner, R-Ohio, said as the White House and Democrats held to their position of agreeing to negotiate only after the government is reopened and the $16.7 trillion debt limit raised.

Republicans pointed to a quote in The Wall Street Journal from an anonymous White House official that “we are winning … It doesn’t really matter to us” how long the shutdown lasts.

At issue in the shutdown is a temporary funding measure to keep the government fully open through mid-November or mid-December.

More than 100 stopgap continuing resolutions have passed without much difficulty since the last shutdown in 1996. But tea party Republicans, their urgency intensified by the rollout of health insurance marketplaces this month, are demanding concessions in Obama’s health care law as their price for the funding legislation, sparking the shutdown impasse with Democrats.

Obama has said he won’t negotiate on the temporary spending bill or upcoming debt limit measure, arguing they should be sent to him free of GOP add-ons. Congress, whether controlled by Democrats or Republicans, routinely sent Obama’s predecessor, George W. Bush, “clean” stopgap spending bills and debt-limit increases.

House Republicans appeared to be shifting their demands, de-emphasizing their previous insistence on defunding the health care overhaul in exchange for re-opening the government. Instead, they ramped up calls for cuts in federal benefit programs and future deficits, items that Boehner has said repeatedly will be part of any talks on debt limit legislation.