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Speaker of the House John Boehner, R-Ohio, walks to the House floor after midnight, Tuesday, Oct. 1, 2013, at the Capitol in Washington. (AP Photo/J. Scott Applewhite)

U.S. House Speaker

made a short statement, took one question, then walked away from a roughly one-minute press conference early Tuesday morning, just more than an hour after the

.

"The House has has made it's position known very clearly," Boehner said just after 1 a.m. ET. "We believe we should fund the government, and we think there ought to be basic fairness for all Americans under Obamacare. The Senate has continued to reject our offers. But under the Constitution, there is a way to resolve this process and that is to go to conference and talk through your differences. I would hope the Senate will accept our offer to go to conference and discuss this so we can resolve this for the American people," he said just after 1 a.m. ET.

He then opened the floor to questions. He was asked what his message was to the 800,000 federal workers who will receive notices they are no longer needed on the job. And does he have a plan for restore back pay?

"The House has voted to keep the government open. But we also want basic fairness for all Americans under Obamacare," he said before leaving the podium.

"Conference" operates after the House and the Senate have passed different versions of a bill. It is exists to draft a compromise bill.