The House of Representatives will make another attempt Wednesday to pass three emergency funding bills after each failed to obtain the required two-thirds majority Tuesday.

The House Rules Committee is scheduled to meet at 10:15 a.m. Wednesday to consider the three measures backed by House Republicans, which are aimed at reopening parks and monuments, continuing veterans’ benefits and allowing the municipal government of the District of Columbia to function.

Unlike on Tuesday, the latest bills will not be treated by House GOP leaders as suspension bills, which means they only need a simple majority vote to pass. On Tuesday, each measure needed 286 votes to pass. The parks funding bill went down by a tally of 252-176, the veterans programs by 264-164 and the D.C. government funding by 265-163.

However, even if the bills pass the House Wednesday, they are almost assuredly doomed in the Senate, where Democrats suggested GOP House members had picked high-profile parts of the government to fund as a cover for their part in forcing a government slowdown, while overlooking other critical areas such as the National Institutes of Health.

"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," Senate Majority Leader Harry Reid said Tuesday night.

The White House has also rejected the bills in advance.

“The president and the Senate have been clear that they won't accept this kind of game-playing, and if these bills were to come to the president's desk he would veto them," said White House spokeswoman Amy Brundage. "These piecemeal efforts are not serious and they are no way to run a government.”

Mike Steel, spokesman for House Speaker John Boehner, fired back, “How does the White House justify signing the troop funding bill, but vetoing similar measures for veterans, National Parks, and District of Columbia? The President can't continue to complain about the impact of the government shutdown on veterans, visitors at National Parks, and DC while vetoing bills to help them. The White House position is unsustainably hypocritical."

The two chambers tried in vain earlier to reach a budget resolution. Shortly after midnight, the House endorsed an approach that delays the federal health care law's individual mandate while prohibiting lawmakers, their staff and top administration officials from getting government subsidies for their health care. They formally urged the Senate to form a conference committee -- a bicameral committee where lawmakers from both chambers would meet to resolve the differences between the warring pieces of legislation.

Meeting Tuesday morning, the Senate rejected the proposal, in a party-line, 54-46 vote.

Both sides dug in, with Republicans insisting that any spending bill include provisions to chip away at ObamaCare, and Democrats refusing to allow it.

Both sides were hard at work blaming the other for the state of affairs.

"It's time for Republicans to stop obsessing over old battles. I mean, I say to my Republican friends, ObamaCare is over. It's passed, it's the law," Senate Democratic Leader Harry Reid said.

President Obama, speaking from the Rose Garden Tuesday afternoon, tried to put pressure on Republicans to allow a "clean" budget bill.

"Republicans in the House of Representatives refused to fund the government unless we defunded or dismantled the Affordable Care Act. They've shut down the government over an ideological crusade to deny affordable health insurance to millions of Americans. In other words they demanded ransom just for doing their job," Obama said.

He noted the GOP did not succeed in shutting down ObamaCare, a large part of which opened officially on Tuesday.

Elsewhere in Washington, House Republicans were pressuring Democratic senators to meet them at the negotiating table to hash out a budget package.

The House appointed "conferees" overnight who would -- if the Senate agrees -- participate in a conference committee to craft a budget bill. Those GOP representatives held a press conference Tuesday to note that Democrats were nowhere to be found at that negotiating table.

"All of us here (are) sitting at a table waiting for the Senate Democrats to join us so we can begin to resolve our differences," House Republican Leader Eric Cantor, R-Va., said.

"The way to resolve our differences is to sit down and talk. And as you can see, there's no one here on the other side of the table," he said.