(CNN) -- The U.S. government shut down at 12:01 a.m. ET Tuesday after lawmakers in the House and the Senate could not agree on a spending bill to fund the government.The two sides bickered and blamed each other for more than a week over Obamacare, the president's signature health care law. House Republicans insisted the spending bill include anti-Obamacare amendments. Senate Democrats were just as insistent that it didn't.Federal employees who are considered essential will continue working. But employees deemed non-essential -- close to 800,000 will be furloughed.Most furloughed federal workers are supposed to be out of their offices within four hours of the start of business Tuesday.President Barack Obama issued a statement early Tuesday to military members and Department of Defense employees about the outcome of the shutdown."Those of you in uniform will remain on your normal duty status," the president said. "Congress has passed, and I am signing into law, legislation to make sure you get your paychecks on time. And we'll continue working to address any impact this shutdown has on you and your families.""To all our DOD civilians--I know the days ahead could mean more uncertainty, including possible furloughs," the president added. "And I know this comes on top of the furloughs that many of you already endured this summer. You and your families deserve better than the dysfunction we're seeing in Congress. ... That's why I'll keep working to get Congress to reopen our government and get you back to work as soon as possible."The shutdown appeared inevitable Monday night as House Republicans acknowledged they can't overcome Senate objections to a proposal that includes provisions aimed at derailing Obamacare.The plan now is to have another vote that would request a conference with the Senate to work out their differences. The move, which would not avert a shutdown, was slammed by Senate Majority Leader Harry Reid.He rejected the House's proposal to meet, saying "we will not go to conference with a gun to our head."See how the Government Shutdown affects OklahomansFor the second time Monday, the Senate rejected a House Republican effort to derail Obamacare tied to a proposal that would avert the shutdown.The Senate voted to table amendments that would have delayed the individual mandate in the health care law and eliminated health insurance premium subsidies for members of Congress, their staffs and the president.In the latest volley of legislative ping pong over a short-term spending plan needed to avoid the shutdown, House Republicans were expected to meet to discuss their next steps."The government is going to shut down ... I don't know for how long," GOP Rep. Devin Nunes of California told CNN while leaving Speaker John Boehner's office.Democratic Rep. Chris Van Hollen said the reason there isn't a budget is because Republicans refused to negotiate months ago."They want to go to conference with 45 minutes left," Van Hollen said late Monday night. "That is a recipe for a government shutdown,"Earlier, Senate Democrats had rejected a House proposal by a 54-46 vote on strict party lines.Obama made a previously unscheduled statement to reporters on Monday afternoon, blasting the attempts by House Republicans to undermine Obamacare that he said threaten to harm the economy with a shutdown."You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, where just because there's a law there that you don't like," the president said.Obama later called Boehner and other party leaders in the House and Senate, the White House said, but a Boehner spokesman indicated there was no breakthrough.