As bickering over a 2014 continuing resolution pushed the government shutdown into its second day on Wednesday, House Republicans showed no signs of letting up on their efforts to derail Obamacare.

Instead, the House Rules Committee will meet Wednesday morning to try and revive a couple of failed piecemeal bills that were rejected by the House a day earlier. Efforts to pass a series of mini-continuing resolutions to restore funding to Veterans Affairs, national parks and the District of Columbia failed to get the two-thirds majority of votes needed under the suspension rule.

The non-controversial measures, including one to fund the National Institutes of Health, will be brought to the floor again under regular rules, with a majority vote needed to pass them.

Even if the measures had made the cut, Democrats said they would reject this approach to keeping the government open, and President Barack Obama said he would veto them.

“Speaker [John] Boehner has the votes to reopen the government and he knows it,” said Senate Majority Leader Harry Reid, D-Nev. “By refusing to let the House vote on the only bill that will reopen the government, Speaker Boehner is singlehandedly 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 reopen the government with Republican and Democratic votes.”

The idea of a piecemeal approach to temporarily fund the government was a suggestion from Sen. Ted Cruz, R-Texas, who took the lead on defunding Obamacare ahead of the budget debate. Cruz, a tea party-backed Republican, recently staged a filibuster in order to prevent cloture on the stopgap measure, much to the ire of his colleagues in both chambers.

“I think we ought to pass continuing resolutions to fund every single priority that President Obama laid out,” Cruz told Fox News’ Bill O’Reilly on Tuesday. “I agree with them. We should go forward and fund the national parks. (...) What I am saying is we should focus on areas of bipartisan agreement."

In a floor speech on Wednesday, Reid taunted House Republicans, saying that “when your last brilliant plan comes from the same person who came up with the dumbest idea ever,” then they should know they are on the wrong track.

The 2013 government shutdown is the first in 17 years, with some 800,000 federal workers are expected to be furloughed.