WASHINGTON — President Barack Obama this week will test whether he still has the sway to keep Washington focused on his own priorities, even as a new Republican-run Congress descends on the Capitol eager to take him on.

Fresh off a two-week vacation, Obama immediately began ramping up for his State of the Union address — his best chance to set the agenda for 2015 on his own terms. Obama will roll out new executive steps and proposals for Congress this week on home ownership, higher education and manufacturing jobs — a similar menu to the one Obama has offered in years past.

Republicans have an entirely different blueprint for the start of the year. In full control of Congress for the first time of Obama’s presidency, they planned an all-out offensive against his policies on immigration, foreign policy and the environment.

In a sign of their divergent paths, just as lawmakers arrive in Washington to start the new Congress this week, Obama was heading out of town. He planned to spend most of the week in Michigan, Arizona and Tennessee showcasing how his own economic policies are fueling the economic recovery.

The State of the Union comes early this year, on Jan. 20, and it is Obama’s first with Republicans in control of both House and Senate.