Although there’s no viable prospect for ending the government shutdown, members of Congress were told today to stick around for weekend votes, caucus meetings and news conferences that might at least promote the illusion — if not the possibility — of progress toward the end of the impasse.

House Republican leaders emerged from their latest caucus meeting Friday to declare they are being much less intransigent than the Democrats, although they offered nothing in the way of public concession other than a willingness to negotiate on things President Barack Obama says are non-negotiable.

“This isn’t some damn game,” Speaker John A. Boehner declared at a news conference. “All we’re asking for is to sit down and to have a conversation about bringing some fairness to the American people under Obamacare.”

Democrats said that, before such talks were worth having, the GOP leadership and even-more-conservative rank and file needed to come up with a coordinated bargaining position. “It’s very hard to negotiate with the Republicans when they can’t negotiate with themselves,” House Minority Leader Nancy Pelosi said on CBS “This Morning.”

House Republican leaders plan to bring to the floor in the coming days as many as 11 more rifle-shot bills to open politically popular slices of the federal system. Among them: the National Weather Service and the Federal Emergency Management Agency (because the year’s first serious threat of an Atlantic hurricane is emerging), the Food and Drug Administration (which says it can’t otherwise meet its food inspection obligations) and the Women, Infants and Children and Head Start nutrition and education programs.

The House already passed five of these miniature continuing resolutions, which Senate Majority Leader Harry Reid has signaled he has no intention of putting to a vote in his chamber because, in his view, the whole government should be reopened and Congress has no business picking programmatic winners and losers.

But another bill the House will soon take up would promise back pay to all 800,000 furloughed federal workers once the standoff ends, presumably including the thousands working on Capitol Hill. There were some indications the Senate might agree to endorse that legislation.

House members were told to expect roll calls on the floor between 10 a.m. and noon Saturday, after which they would be free to go back to their districts until Monday evening.

Reid did not lay out any such timetable, but has told senators to be ready for votes all weekend. Absent some budget agreement, though, the only roll calls both sides have agreed to hold are to confirm of a pair of federal trial court judges in Illinois.

Obama was scheduled to leave Saturday for economic summits next week in Indonesia and Brunei, but those trips have both now been canceled — a concession not only to the need for the president to be available if there’s any movement on the overdue spending and impending debt limit talks, but also to the public relations challenges of spending millions on a presidential trip halfway around the word when so much of the government is shuttered.