WASHINGTON—The U.S. government moved to within hours of its first shutdown since 1996, as House Republicans redoubled their drive early Sunday to delay the new health care law and Senate Democrats stood firm against changing the law as a condition of funding federal departments.

The standoff left little prospect that Congress could reach agreement on terms for funding the government by midnight Monday, when the current fiscal year expires. A shutdown would leave essential services operating but prompt federal agencies to suspend many functions and furlough hundreds of thousands of workers.

On a 231-192 vote, the House early Sunday passed a one-year delay of the health law, often called Obamacare, and attached it to a plan to fund the government through Dec. 15. The legislation now goes to the Senate. It also includes a provision repealing a tax on medical devices intended to help finance the health law, which the House approved on a 248-174 vote.

But Senate Majority Leader Harry Reid (D., Nev.), in a statement issued hours before the House took up the bill, pledged to strip out the health provisions. He denounced the GOP vote as "pointless" and declared the impasse to be back at "Square 1."

The White House said that if the House bill reached President Barack Obama, who championed the health law, he would veto it.