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House Republicans were engaged in a last-ditch effort to avert a government shutdown Monday, calling on the Senate to negotiate with them directly and resolve their differences over ObamaCare.

But as Congress fast-approached a midnight deadline, the two sides appeared no closer to an agreement.

“Republicans are still playing games,” Senate Majority Leader Harry Reid declared on the Senate floor.

The Senate earlier in the night rejected the latest Republican counteroffer that would rein in ObamaCare while still funding the government past midnight.

House Republicans have started floating the possibility of taking their disagreement to what’s known as a conference committee – a bicameral committee where lawmakers from both chambers would meet to resolve the differences between the warring pieces of legislation.

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    “It means we're the reasonable, responsible actors trying to keep the process alive as the clock ticks past midnight, despite Washington Democrats refusal - thus far - to negotiate,” a GOP leadership aide said.

    Reid, though, said the Senate would not agree to the approach unless and until the House approves a “clean” budget bill.

    Lawmakers are facing a midnight deadline to reach an agreement on a government spending bill, or the government begins to shut down. The rhetoric was getting more heated as the deadline neared.

    “They’ve lost their minds,” Reid said of Republicans, in rejecting the latest proposal.

    “Senate Democrats have made it perfectly clear that they’d rather shut down the federal government than accept even the most reasonable changes to ObamaCare,” Senate Republican Leader Mitch McConnell countered.

    The latest House bill, which the chamber backed on a 228-201 vote, would have delayed the law's individual mandate while prohibiting lawmakers, their staff and top administration officials from getting government subsidies for their health care.

    The Senate voted 54-46 along party lines to reject it.

    Amid the drama, President Obama said he's holding out hope that Congress will come together "in the 11th hour."

    A shutdown "does not have to happen," Obama said, during remarks at the White House.The president has called the top four congressional leaders, including House Speaker John Boehner, though no breakthrough was reported.

    At this point, it’s unclear what common ground the two sides can find. The latest GOP proposal stirred dissension in the ranks, with some lawmakers reluctant tohurt their own staff by taking away additional subsidies for their health care costs. According to the site Legistorm, the average House staffer salary is under $60,000.Twelve House Republicans peeled off in the latest vote to oppose the bill.

    Congress has until midnight to craft a spending bill, or else the government will begin to wind down. Both sides, though, are digging in deep.

    The Senate earlier Monday rejected a GOP proposal that would delay the health care law by one year and repeal an unpopular medical device tax. Reid warned Republicans not to fiddle with the spending bill any more.

    Ahead of the House vote, Obama said Congress can avert a shutdown by passing a straight budget bill without "extraneous and controversial demands."

    Obama warned that a shutdown would hurt all Americans, noting that the federal government is the country's largest employer."A shutdown will have a very real economic impact on real people, right away," Obama said.

    A prior Republican effort to include a provision defunding ObamaCare in the budget bill failed. House Republicans then voted, early Sunday, to add amendments delaying the health care law by one year and repealing an unpopular medical device tax.

    The Senate, in a 54-46 vote, rejected those proposals on Monday afternoon.

    In a rare note of optimism, Obama said earlier Monday that he's "not at all resigned" to a shutdown.

    But the path forward is not clear. With nothing less than the operation of government on the line, the battle in Congress over ObamaCare was shaping into a test of wills.

    Reid has outright stated he will not accept any measures that undermine the health care law as part of the budget bill. With the bill back on the House side, Boehner and Reid now face off with their final set of chess moves in a very narrow time frame. Lawmakers have until midnight to strike a deal.

    Reid wants Boehner to simply call up the "clean" budget bill, without any ObamaCare provisions, and presumably let it pass with majority Democratic support.

    "I have a very simple message to John Boehner: let the House vote," Reid said Monday.

    But at this stage, a shutdown is highly possible, and congressional leaders are hard at work trying to assign blame. Democrats have already labeled this a "Republican government shutdown." But Republicans on Sunday hammered Reid and his colleagues for not coming back to work immediately after the House passed a bill Sunday morning.