With the government shutdown closing national monuments and sending federal office workers home, House Republicans changed tactics Tuesday and tried to pass individual spending bills that they said would restore money to high-profile programs such as veterans affairs, national parks and the Smithsonian Institution.

But House Democrats, backed by a presidential veto threat, blocked the bills, saying that while they supported the spending, it was unfair for Republicans to make them pick and choose from popular programs.

The nighttime votes were the capstone to the first full day of the first government shutdown in 17 years, and highlighted the glaring lack of middle ground for a compromise to be reached.

“Just another wacky idea,” said Senate Majority Leader Harry Reid, Nevada Democrat, dismissing House Republicans’ latest gambit just as he did with three previous efforts to fund the government while trying to put a dent in Obamacare.

Senate Democrats passed a bill that would fund the government, including Obamacare, through Nov. 15, and vowed to accept nothing less. Republicans have tried to offer nine proposals to fund all or parts of the government, but each has been rejected.

Democrats said if House leaders would bring the Senate bill to the floor, it would pass — but Republicans have refused to call for a vote.

While all sides said they tried to avoid a shutdown, the first day didn’t seem to scare many of them away from their staunch positions.

At least for the first day, the shutdown amounted to more of a slow burn than a raging fire torching treasured programs.

Indeed, the stock market, which dipped Monday as the shutdown deadline approached, rebounded Tuesday. Although an estimated 800,000 federal workers were sent home to wait out the shutdown, lawmakers seemed surprised that there wasn’t more of an outcry from voters.

As lawmakers took stock of the first day, they also eyed a debt fight that looms in two weeks. Many analysts predict that will be an even bigger battle, covering not just basic spending but also taxes and the big entitlement programs such as Social Security and Medicare.

On Tuesday, House Republicans emerged from a closed-door meeting saying they felt like they were in a stronger position than earlier in the week, when they appeared to be casting about for a solution that would allow them to save face.

“The mood in there was good. It was positive, it was unified — it was more unified than it was a day before,” said Rep. Steve King, an Iowa Republican who is among the more conservative House members and who pushed for the party to take a strict line on halting the Affordable Care Act.

House Speaker John A. Boehner, Ohio Republican, also appeared to be on firmer footing with his conference, even earning the support of Republicans who have been opponents in the past. Rep. Steve Stockman, a Texas Republican who worked against making Mr. Boehner the speaker of the House in January, showered praise on the party leader.

“I recognize that how difficult it is to be the leader of so many independent, conservative-thinking congressmen, but today I am proud to say that Boehner has shown true leadership and unified the party,” he said. “I want to openly express my gratitude for his fortitude in this current government gridlock.”

A day earlier, Mr. Boehner had to head off a revolt within his conference, pleading with lawmakers to stick with him as the House took vote after vote in its battle with the Senate.

The frenzied pace of Monday gave way to legislative lethargy Tuesday.

The House spent most of the day in recess but returned late in the evening to try its piecemeal strategy with three bills. One of them would have funded the Department of Veterans Affairs; another would have restored money for the National Park Service, the Smithsonian Institution, the United States Holocaust Memorial Museum and the National Gallery of Art; and a third would have given the District of Columbia the right to spend its own tax money during the shutdown.

Democrats said they supported all of those ideas but couldn’t accept choosing priorities.

“As outrageous as all of this is, the worst tragedy is what it does to our capital city,” said Rep. James P. Moran, Virginia Democrat. “In the District of Columbia, D.C. residents have paid for their government and yet this shutdown refuses to even let them use their own revenue to run their government.”

Delegate Eleanor Holmes Norton, a Democrat who represents the District, said Mayor Vincent C. Gray has “cobbled together” the city’s contingency funds to keep the government open, but those funds will run out in a couple of weeks if Congress fails to act.

“If federal workers should not be punished because Congress did not do its job, surely a shutdown of the District of Columbia would have punitive effects no one can condone,” Ms. Norton said in her prepared remarks. “No Republican or Democrat desires the unintended effect of shutting down the local government only because D.C.’s local balanced budget has not cleared the Congress.”

Mr. Gray has deemed all city employees essential, meaning he will try to keep everyone including janitors and librarians on the job.

But the bill in Congress to grant him more authority failed to garner the two-thirds vote needed to pass under special expedited rules. Most Democrats opposed the bill.

Democrats also opposed the veterans and parks bills.

“This isn’t about the parks. They’re using parks as a pawn. This is about defunding the Affordable Care Act,” said House Minority Leader Nancy Pelosi, California Democrat. “It’s not going to happen.”

Republicans said they had to resort to the piecemeal approach because the Senate rejected all of their other offers — including a request to enter into formal negotiations in a conference committee.

Senate Democrats rejected that proposal early Tuesday in another party-line vote, saying they will not begin to negotiate until the House relents and agrees to a funding bill with no strings attached.

“All they have to do is accept what we already passed,” Mr. Reid said.

House Republicans have long argued that the annual spending bills — and the debt limit fight — are leverage points that should be used to overcome a Democratic Senate that has blocked most of the Republican agenda the past two years.

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