WASHINGTON — President Barack Obama brought top lawmakers to the White House on Wednesday as Republicans rejected Democratic demands to vote on legislation ending a two-day partial government shutdown without changes to the nation’s 3-year-old health care law.

Despite the meeting, White House press secretary Jay Carney said sharply that Obama “will not offer concessions to Republicans in exchange for not tanking the economy.”

With the nation’s ability to borrow money soon to lapse, Republicans and Democrats alike said the shutdown that has idled some 800,000 federal workers could last for two weeks or more, obliging a divided government to grapple with both issues at the same time.

House Republicans brought a handful of bills to the floor to reopen portions of the government, including veterans’ programs, parks and the National Institutes of Health. Democrats labeled that a piecemeal approach and rejected it, and the White House threatened to veto the measures in the unlikely event they made it to Obama’s desk.

“What we’re trying to do is to get the government open as quickly as possible,” said the House majority leader, Rep. Eric Cantor, of Virginia. “And all that it would take is us realizing we have a lot in agreement.”

Democrats were scathing.

“The American people would get better government out of Monkey Island at the local zoo than we’re giving them today,” said Rep. John Dingell, of Michigan.

The stock market ended lower Wednesday as Wall Street CEOs, Europe’s central banker and traders pressed for a solution before serious damage is done to the economy. Chief executives from the nation’s biggest financial firms met Obama for more than an hour Wednesday, some of them plainly frustrated with the tactics at play in Congress and with the potential showdown coming over the debt limit.

“You can relitigate these policy issues in a political forum, but we shouldn’t use threats of causing the U.S. to fail on its obligations to repay its debt as a cudgel,” Lloyd Blankfein, CEO of Goldman Sachs, said after the meeting.

An attempt by Democrats to force shutdown-ending legislation to the House floor failed on a 227-197 vote, with all Republicans in opposition. That left intact the tea party-driven strategy of demanding changes to the nation’s health care overhaul as the price for essential federal financing. Late in the afternoon, leading lawmakers filed into their meeting with Obama.

The Republican National Committee announced it would pay for personnel needed to reopen the World War II Memorial, a draw for aging veterans from around the country that is among the sites shuttered. In a statement, party chairman Reince Priebus challenged Democrats “to join with us in keeping this memorial open.”

As it turned out, more than 125 World War II veterans from Mississippi and Iowa who were initially kept out of the memorial Tuesday were escorted to the site with the help of members of Congress.

Officials made further arrangements to allow veterans groups into the memorial during the shutdown.

A sampling of federal agencies showed how unevenly the shutdown was felt across the government.

The Environmental Protection Agency and Department of Housing and Urban Development listed only six percent of their employees as essential, and therefore permitted to work during the impasse.

James R. Clapper, director of national intelligence, said about 70 percent of civilian employees in agencies under his control had been sent home.

By contrast, about 86 percent of employees of the Department of Homeland Security remained on the job, and 95 percent at the Veterans Affairs Department.

One furloughed employee, meteorologist Amy Fritz, said, “I want to get back to work.” At a news conference arranged by congressional Democrats, the 38-year-old National Weather Service employee said she has more than $100,000 in student loan debt and is looking at ways to cut her budget.

In an interview with CNBC before meeting with lawmakers, Obama said he would not negotiate with Republicans until the government is reopened and Congress votes to raise the debt limit.

“If we get in the habit where a few folks, an extremist wing of one party, whether it’s Democrat or Republican, are allowed to extort concessions based on a threat (to)  undermine the full faith and credit of the United States, then any president who comes after me, not just me, will find themselves unable to govern effectively,” he said.

“The White House said Obama would have to truncate a long-planned trip to Asia, calling off the final two stops in Malaysia and the Philippines.

The shutdown also intruded into the race for governor of Virginia.

Terry McAuliffe, the Democrat, said he supported legislation to guarantee retroactive pay for furloughed federal employees. The Republican contender, Ken Cuccinelli, called on members of Congress to decline their pay as long as the shutdown lasts.

Obama’s call to lawmakers to meet drew a quizzical response from Senate Republican leader Mitch McConnell. A spokesman, Don Stewart, said, “we’re a little confused as to the purpose.”

Boehner was “pleased the president finally recognized that his refusal to negotiate is indefensible,” said his spokesman, Brendan Buck. “It’s unclear why be having this meeting if it’s not meant to be a start to serious talks between the two parties.”

Responding to the House’s call for formal negotiations on the shutdown, health care and other issues, Senate Majority Leader Harry Reid wrote to the speaker to say he would agree, but only if the House first agreed to reopen the government.

Boehner rejected that.

The House sidetracked legislation Tuesday night to reopen some veterans programs, the national parks and a portion of the Washington, D.C., municipal government. All three bills fell short of the two-thirds majority needed when Democrats voted overwhelmingly against this.

Republicans tried again, this time under rules requiring only a simple majority, and passage seemed likely. They added two more measures to the list, one to provide money for the National Guard and Reserves, and the other for the National Institutes of Health.

The NIH bill was added to the day’s agenda after Democrats said seriously ill patients would be turned away from the facility’s hospital of last resort, and no new enrollment permitted in experimental treatments.

Democratic Rep. Louise Slaughter of New York said the Republican response was a ploy. “Every time they see a bad headline they’re going to bring a bill to the floor and make it go away,” she said.

Some Republicans took obvious pleasure in the rough rollout Tuesday of new health insurance markets created under Obama’s health care law. Widespread online glitches prevented many people from signing up for coverage that begins in January.

Rep. Trey Radel of Florida said a 14-year-old could build a better website “in an afternoon in his basement.”

Not all Republicans felt the same.

Rep. Peter King, R-N.Y., accused tea party-backed lawmakers of trying to “hijack the party” and said he senses that a growing number of House Republicans — perhaps as many as 100 — are tired of the shutdown that began Tuesday morning and will be meeting to look for a way out.

An earlier attempt by Republican dissidents to take control of the floor and vote alongside Democrats to reopen the government fizzled badly earlier in the week, and it was unclear whether a new attempt could gain traction.

At issue is the need to pass a temporary funding bill to keep the government open since the start of the new budget year on Tuesday.

Congress has passed more than 100 temporary funding bills since the last shutdown in 1996, almost all of them without controversy. The streak was broken because conservative Republicans have held up the current measure in the longshot hope of derailing or delaying Obamacare, just as the health insurance markets at the heart of the law opened on Tuesday.

Associated Press writers Andrew Taylor, Donna Cassata, Henry Jackson, Julie Pace, Jessica Gresko, Darlene Superville and Seth Borenstein contributed to this story