WASHINGTON — After two embarrassing failed votes last week, House Republicans regrouped Tuesday and voted to open debate on a package of spending bills they hope will unlock votes to keep the government from shutting down at the end of the week.

The rule passed 216-212, with Rep. Marjorie Taylor Greene, R-Ga., as the sole Republican to vote against it.

A federal shutdown early Sunday is still highly likely given broad disagreements between the GOP-controlled House and the Democratic-led Senate over funding levels and aid for Ukraine.

But Speaker Kevin McCarthy, R-Calif., believes that if he can rally his troops behind four partisan appropriations bills this week, he can put Republicans in a better negotiating position with the congressional Democrats and the White House heading into a potential shutdown.

“We’re going to work through appropriations bills this week. … We’ll have a process to get through a large chunk of funding, significantly more than the Senate’s been able to get through,” said a top McCarthy ally, Financial Services Chairman Patrick McHenry, R-N.C. “And that should put us in a better negotiating position for what is inevitably going to be the end-of-year negotiations around funding the government.”

The four bills would fund the departments of Defense, Homeland Security and Agriculture, as well as the State Department and foreign operations. Adhering to the demands of House conservatives, the bills would cut billions of dollars despite a bipartisan debt and spending deal this year between McCarthy and President Joe Biden.

McCarthy said after Tuesday’s vote that he plans to bring a short-term funding bill, known as a continuing resolution, or CR, to the floor this week, even though a number of conservatives in his conference have vowed to vote it down.

McCarthy told reporters the CR would come to the floor “probably on Friday.”

The Senate on Tuesday evening introduced its own CR, which does not include steep cuts House Republicans want and does include roughly $6 billion in Ukraine aid that many House Republicans oppose.

McCarthy criticized the bipartisan Senate measure, telling reporters it was “wrong” for senators to include Ukraine funding in a short-term funding bill. “They’re picking Ukraine over Americans,” he said.