WASHINGTON — Not wasting any time, new Senate Majority Leader Mitch McConnell and President Barack Obama are setting course for showdowns over health care, a big oil pipeline, immigration policy and financing of the agency that tries to protect the U.S. from terrorists.

At the same time, both insist they are eager for compromise — if only the other side would give in.

“It seems with every new day, we have a new veto threat from the president,” McConnell, R-Ky., complained Wednesday, his second day as Senate leader. Republicans won control of the chamber in the November elections, and strengthened their hold on the House.

With the 114th Congress just getting underway, the White House already has announced that Obama stands ready to veto three bills that Republicans hope to rush through. One would allow construction of the Keystone XL pipeline to bring oil from Canada. Another weakens Obama’s signature health care law, by increasing the definition of a full-time employee who must be offered health coverage at work to 40 hours from the current 30. The third would alter a key provision of the 2010 Dodd-Frank overhaul of financial services regulations.

“The president is not going to set the agenda for us here in the Senate,” McConnell told reporters.