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The Senate returns to Washington on Monday, opening a 2016 in which Republicans will move cautiously on the legislative front to try to protect their endangered incumbents and their Senate majority.

The first order of business is to approve the long-delayed nomination of Luis Felipe Restrepo of Pennsylvania to the United States Court of Appeals for the Third Circuit, a relatively rare vote on an appeals court judge given Republican reticence to allow President Obama to fill more judicial vacancies in his final months.

Much of the Senate’s attention in the early days will be devoted to mapping out an agenda for the year. After the State of the Union address on Tuesday night, Senate Republicans will travel to Baltimore for meetings with their House counterparts to plot a joint approach.

Senator Mitch McConnell of Kentucky, the majority leader, has been clear that his top priority is to avoid making a difficult re-election year even harder for Senate Republicans in blue and purple states. He wants to focus on the unglamorous but less risky business of slogging through the 12 annual appropriations bills.

“This may be a little bit boring to the public, but we haven’t passed every single bill that runs the government, the appropriation bills, since 1994,” Mr. McConnell said on Sunday on ABC’s “This Week.”

“I think we ought to on a bipartisan basis step up to the challenge of getting every single bill that funds the government passed individually, not in a big clump of bills at the end, and get it on the president’s desk,” he said.

This year will also be the last in the Senate for Mr. McConnell’s counterpart — Senator Harry Reid of Nevada, the Democratic leader, who is retiring. Of course he will still have some say in what the Senate does — or doesn’t do — this year.