"Get us through this six weeks and then let's sit down and figure out how we pay our debts and bring down federal spending," McCaskill of Missouri, said on MSNBC.
Republicans planned to continue pursuing their latest strategy: muscling bills through the House that would restart some popular programs.
Votes were on tap for restoring funds for veterans and paying members of the National Guard and Reserves. On Wednesday, the chamber voted to finance the national parks and biomedical research and let the District of Columbia's municipal government spend federally controlled dollars.
Democrats demanded that the entire government be reopened, and the White House and Senate Majority Leader Harry Reid, D-Nev., made clear that the GOP's narrower bills have no chance of survival. They said the strategy showed that Republicans were buckling under public pressure, with Rep. Louise Slaughter, D-N.Y., saying groups like veterans were being "used as a pawn in this cynical political game."
Republicans countered that Democrats were being inflexible and were to blame for the continued closure of programs the GOP was trying to reopen. A favorite target was Reid, who has made clear that the Senate will be a graveyard for the Republican effort.
"The Senate's refusal to work with the House is an all-time low," Rep. Trey Radel, R-Fla., said.
Reid told reporters that Obama and Democrats are "locked in tight" on not diluting the health care law.
In an interview afterward, Senate Minority Leader Mitch McConnell, R-Ky., scoffed at the president's stance.
"He can't get his way exactly the way he wants it because he doesn't control the entire government," McConnell said on CNBC's "The Kudlow Report."
Democrats continued lambasting Boehner and freshman Sen. Ted Cruz, R-Texas, the tea party hero who has helped sell fellow conservatives in both chambers on keeping the government shuttered until Obama retreats on his coveted health care law.
Rep. Jim Jordan, R-Ohio, and other House conservatives said they met with Cruz and other Senate conservatives Wednesday to update each other on what was happening.
"We think we just have to keep talking about our message, which is real simple: 'Treat people fairly,'" Jordan said.
Republican leaders and many rank-and-file GOP lawmakers, especially in the Senate, had been reluctant to link demands for curbing the health care law to legislation keeping government open, concerned that voters would blame Republicans for any shutdown.
But Wednesday, Republicans solidly opposed an unsuccessful Democratic move to force the House to vote on a Senate-passed bill keeping government open until Nov. 15 without any strings on the health care law.
"Now that we've jumped off the cliff, lit ourselves on fire, we've entered the valley of death," said Rep. Devin Nunes, R-Calif., who has criticized the conservatives' strategy. "So now we've got to keep running and we have to hold together."
The House has approved legislation keeping the entire government funded through Dec. 15. It also would impose a one-year delay in the health care law's requirement that individuals buy health insurance, which would threaten to cripple the program, and block federal subsidies for health coverage bought by lawmakers and their staff.
As the politicians battled, mail continued to be delivered, air traffic controllers remained at work and payments were being made to recipients of Social Security, Medicare, Medicaid and unemployment benefits.
Taxes were still due, but lines at IRS call centers went unanswered.
Halted were most routine food inspections by the Food and Drug Administration and some loan approvals for many low- and middle-income borrowers were thrust into low gear by the Housing and Urban Development Department. National parks were closed.
Workers were furloughed based on how essential their jobs were to the nation: Only 3 percent of NASA employees were kept on, while 86 percent at the Homeland Security Department were working.
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