House Republicans showed no signs of caving as the first day of the government shutdown wound down. They vowed to continue pressing Senate Democrats to negotiate over spending even as they began advancing narrowly tailored spending bills that could reduce the shutdown’s impact.

Republicans on Tuesday introduced three appropriations bills to fund programs for military veterans, national parks and museums and the government of the District of Columbia. But the measures failed because House rules required each bill to garner a two-thirds vote and Democrats surprised GOP leaders by refusing to back the measures.

Even if the House Democrats had failed to block the bills, the measures have little chance of surviving. Senate Democrats already declared them dead on arrival and President Obama threatened to veto them.

But the intensity of the opposition only emboldened House Republicans, who believe Democrats will find it difficult to explain to voters why they refused to fund such popular programs.

GOP leaders will reintroduce the budget bills Wednesday, but under different rules that would allow the Republican majority to pass them without Democratic support.

Despite polls showing that voters are more likely to blame them for the shutdown, House Republicans head into Day Two confident in their strategy and convinced public pressure will eventually force Senate Democrats to the bargaining table.

“Our argument has been the same for the last 24 hours: We want to meet face to face with the folks from the Senate and be able to work things out,” said Republican Policy Chairman James Lankford, R-Okla. “It’s kind of sad to me, quite frankly, that they can say we’re not going to meet face to face.”

The Capitol went quiet Tuesday evening as House Republicans and Senate Democrats prepared for the possibility of a lengthy government shutdown. Senate Democrats are insisting on a "clean" budget bill that funds the government but doesn't touch Obamacare. House Republicans, who are insisting on changes to Obamacare in exchange for approving the budget bill, are demanding Democrats meet with them in a conference committee to resolve differences over the bills.

To underscore Democrats' resolve, Senate Majority Leader Harry Reid, D-Nev., adjourned the Senate early Tuesday evening, long before the House could even vote on the three appropriations bills. After the House voted, Reid issued a statement warning House Speaker John Boehner that a "clean" budget bill was the only path to resolving the stalemate and reopening the government.

"Speaker Boehner has the votes to re-open the government and he knows it,” Reid said. “By refusing to let the House vote on the only bill that will re-open the government, Speaker Boehner is single-handedly keeping the government shut down. It is time for Speaker Boehner to stop the games, think about the people he is hurting, and let the House pass the Senate's bill to re-open the government with Republican and Democratic votes."

About a dozen House Republicans support taking up a "clean" budget bill and others are willing to drop the strategy of defunding Obamacare in a budget bill needed to keep the government running. But Republican House leaders and most of their rank-and-file members are betting that the budget bills will at least force Democrats to negotiate with them.

Their confidence in this strategy appears to have diminished the urgency to end the shutdown, at least in the short term. Senate Democrats are equally unified and confident.

“We may have gotten ourselves in a position where we can’t budge on a clean CR and they can’t budge on Obamacare," Rep. Mike Simpson, R-Idaho, said. "Then what do you do?"