ALAN FRAM, Associated Press

WASHINGTON (AP) — The government limped into a third day of partial shutdown Thursday with no sign of a way out after a White House conversation between President Barack Obama and top congressional leaders seemed only to harden the stances of Democrats and Republicans.

"The president remains hopeful that common sense will prevail," the White House said in a written statement after the unproductive meeting about the political standoff that has idled 800,000 federal workers and halted an array of services Americans expect from their government.

House Speaker John Boehner, R-Ohio, complained to reporters that Obama used the meeting simply to declare anew that he won't negotiate over his health care law.

House Republicans, pushed by a core of tea party conservatives, are insisting that Obama accept changes to the health care law he pushed through three years ago as part of the price for reopening all of government. Obama refuses to consider any deal linking the health care law to routine legislation needed to extend government funding.

"We're probably through negotiating with ourselves," Rep. Jeb Hensarling, R-Texas, chairman of the House Financial Services Committee, said Thursday on MSNBC.

Republicans who initially sought to defund the health care law in exchange for funding the rest of government have gradually scaled back their demands but say they need some sort of offer from Obama.

Expressing frustration after Tuesday night's White House meeting, Boehner said: "All we're asking for here is a discussion and fairness for the American people under Obamacare."

The White House said Obama would be happy to talk about health care — but only after Congress moves to reopen the government "and stop the harm this shutdown is causing to the economy and families across the country."

The lack of progress fanned the widening impression that the shutdown dispute could persist into mid-October and become tangled with an even more consequential battle over the debt limit. The Obama administration has said Congress must renew the government's authority to borrow money by Oct. 17 or risk a first-ever federal default, which many economists say would dangerously jangle the world economy.

The shutdown stalemate is already rattling investors. Stock markets in the U.S. and overseas faded Wednesday, and Europe's top central banker, Mario Draghi, called the shutdown "a risk if protracted." Leading financial executives met with Obama, and one, Goldman Sachs CEO Lloyd Blankfein, said politicians should not use a potential default "as a cudgel."

Democratic Sen. Claire McCaskill said the House could easily defuse the worsening situation.

"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 Thursday.

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.