(Adds McConnell remarks from CNN interview)
By Patricia Zengerle and Julia Edwards
WASHINGTON/HONOLULU, Jan 4 (Reuters) - Republicans take full control of the U.S. Congress this week with an agenda of trying to force approval of the Keystone XL oil pipeline and push back on President Barack Obama's sweeping policy shifts on Cuba and immigration.
After years of battles over the budget and other issues, further clashes loom as Republicans who already control the House of Representatives take over the Senate majority on Tuesday after wins against Obama's Democrats in November's midterm elections. Angry over the president's moves last year to bypass Congress on issues such as immigration, Republicans have promised to fight him on a range of issues.
Obama has vowed to use his veto pen if Republicans pass legislation he opposes, but he has said he believes he may be able to forge common ground with them in some areas, including free trade, overhauling the tax code and boosting infrastructure spending.
Reaching deals won't be easy amid deep mistrust on both sides.
"To suddenly claim you're going to work with members of Congress after years of ignoring them is rather ludicrous," said Kevin Smith, a spokesman for Republican House of Representatives Speaker John Boehner.
Republican Mitch McConnell, who will become the Senate majority leader, said the American people expect compromise on key issues despite divided government.
"They want us to look for things to agree on and see if we can make some progress for the country," he said in a pre-recorded interview aired on CNN's State of the Union program on Sunday.
But issues facing Congress will likely be contentious.
McConnell has said the first item on his agenda will be legislation to force approval of TransCanada Corp's Keystone XL pipeline. The pipeline, which has been under review by the Obama administration for years, would help transport oil from Canada's oil sands to the U.S. Gulf Coast. Many Democrats see the project as a threat to the environment but supporters say it will create jobs and increase North American energy security.
A similar bill on Keystone failed late last year and it is unlikely that Republicans, even with their new majority, could muster the votes needed to overcome an Obama veto. The new Senate Energy Committee Chairwoman, Lisa Murkowski, plans a vote on Thursday by her panel on the issue.
As the new Congress convenes, Obama will set out on a three-day road trip on Wednesday to Michigan, Arizona and Tennessee to tout his economic record and highlight his own agenda for 2015.
Republican aides said efforts to weaken Obama's signature healthcare law were also high on their priorities.
Another early legislative fight will come when Congress considers funding for the Department of Homeland Security. A $1.1 trillion government spending bill passed in mid-December funds government through September, except for the DHS, which is funded only until Feb. 27. That was an effort by conservative Republicans to block money for implementation of Obama's executive order that grants temporary relief from deportation to some undocumented immigrants.
Republicans have also discussed using the fight over the homeland security agency as a vehicle for challenging Obama's landmark move last month to normalize ties with Cuba. (Additional reporting by Robert Rampton, Timothy Gardner and Patrick Rucker in Washington; Writing by Patricia Zengerle, Editing by Caren Bohan/Frances Kerry/Susan Fenton)