WASHINGTON — The Senate was voting late Sunday on the first steps to end the 40-day government shutdown after a group of moderate Democrats agreed to proceed without a guaranteed extension of health care subsidies, angering many in their caucus who wanted to continue the fight.

The group of three former governors — New Hampshire Sen. Jeanne Shaheen, New Hampshire Sen. Maggie Hassan and Independent Sen. Angus King of Maine — said they would vote to reopen if the Senate passed three annual spending bills and extend the rest of government funding until late January.

Senate Majority Leader John Thune, R-S.D., endorsed the deal Sunday night and called an immediate vote to begin the process of approving it.

“The time to act is now,” Thune said.

The deal also would include a future vote on th

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