A cordoned off area outside the US Capitol in Washington.Yegor Aleyev | TASS | Getty ImagesThe House passed a one-week government funding extension Wednesday as Congress tries to buy time to strike broad spending and coronavirus relief deals.The measure, which passed in a 343-67 vote, would keep the federal government running through Dec. 18. Many operations will shut down amid the raging pandemic if lawmakers fail to approve a funding bill before Saturday.The legislation heads to the Senate, where Majority Leader Mitch McConnell, R-Ky., has indicated he aims to pass it before the deadline. The Senate could try to approve it as soon as Thursday.Congressional leaders hope to reach agreement on an omnibus spending package to fund the government through Sept. 30. Appropriators have come to terms on an overall $1.4 trillion price tag but have not yet agreed on exactly where the money will go.McConnell and House Speaker Nancy Pelosi, D-Calif., have said they want to attach pandemic aid measures to the full-year spending bill.Democratic leaders hope bipartisan talks among rank-and-file lawmakers on a $908 billion coronavirus rescue package will lead to legislation that can pass both chambers of Congress. Treasury Secretary Steven Mnuchin sent a $916 billion offer to Pelosi on Tuesday, but she and Senate Minority Leader Chuck Schumer, D-N.Y., rejected it because it does not include supplemental federal unemployment payments.McConnell on Tuesday also called for lawmakers to drop demands for liability protections and state and local government aid as part of a year-end relief bill. Democrats have opposed the Republican leader’s push to give companies immunity from coronavirus-related lawsuits, saying it would harm employees who work for needlessly reckless companies.While Democrats and many Republicans back new state and local support to avoid layoffs among first responders and teachers, McConnell and the White House have argued the money will go to governments that have not managed their finances wisely.Subscribe to CNBC on YouTube.