(Adds details, quotes starting in fourth paragraph.)
By Richard Cowan
WASHINGTON, Dec 4 (Reuters) - U.S. Republicans, outraged with President Barack Obama for easing deportations of millions of undocumented residents, plan legislation in 2015 strengthening the U.S.-Mexican border to discourage illegal immigration.
The move, likely to come early next year according to House Republican leadership aides, may lead to other steps the House of Representatives could contemplate to repair parts of U.S. immigration law.
When legislation materializes, it would follow a year and half of congressional inactivity in the aftermath of the passage of a sprawling Senate bill backed by Obama but killed by the House.
"I think there is the realization...that this issue is not going away," said Republican Representative Mario Diaz-Balart, who has labored to write broad immigration legislation.
House Homeland Security Committee Chairman Michael McCaul likely will oversee the effort, according to leadership aides. McCaul has pushed legislation imposing tough standards for border apprehensions.
Given the House's rejection of the Senate's work in 2013, a strategy is emerging for 2015 to have the House take the lead in the hope of making better progress.
The 2013 Senate bill's pathway to citizenship for millions of undocumented residents was a lightning rod for opposition.
"I want it to start in the House," said Republican Senator John McCain, a leading immigration reform proponent.
McCain said bills improving border security, establishing an online system for companies to check their workers' immigration status and expanding visas for high-tech foreign workers could be first out of the gate. The latter two are important to U.S. businesses.
Senior House Republican aides said it was unclear what bills might move next year beyond border security.
Republicans hope to gain more control of the immigration debate as they will hold majorities in the House and Senate for the first time since 2006.
They need to improve their standing with Hispanic-American voters as the party strives to capture the White House in 2016.
Passing tougher immigration measures will be difficult, though, as Democratic votes will be needed.
Obama warned business leaders this week that "it's going to be hard, I think, for me and for other Democrats" to support piecemeal legislation that deals with the concerns of business but does not address undocumented Americans.
One leading Democrat on immigration, Representative Zoe Lofgren, was asked if she could support a Republican border security bill, for example.
"It depends on what it is," Lofgren said, adding Republican Representative "Steve King wants to do a (border) wall with electrified wire...I don't think that's a winning vote."
Ultimately, Republicans must address the approximately 12 million undocumented residents living in the United States for extended periods, McCain and Diaz-Balart said.
Many Republicans argue that allowing them to stay in the U.S. rewards law-breakers.
Meanwhile, House Republican leadership is more conservative with the recent election of Representative Steve Scalise to the third-ranking position. Scalise opposes giving legal status to undocumented residents.
Furthermore, the House immigration debate could unfold as a seasonal spike of illegal migration from Central America gets underway. Last summer's arrival of tens of thousands of unaccompanied minors stoked tensions between Republicans and immigration advocates.
For legislation to succeed in 2015, "a lot of things have to line up and they're not lined up now," said one Republican congressman who asked not to be identified. (Editing by Caren Bohan, Sandra Maler and Alan Crosby)