WASHINGTON -- President Barack Obama's announcement of immigration changes that will protect nearly 5 million people living in the U.S. illegally from deportation has infuriated Republicans, but has also left them scrambling for a response that won't undermine their prospects in the 2016 presidential election.

Obama's measure, which will make nearly half of those living the U.S. illegally eligible for work permits, has been criticized by Republicans as an amnesty for lawbreakers and abuse of presidential powers.

In a news conference Friday, House Speaker John Boehner accused Obama "damaging the presidency itself" with his unilateral action on immigration.

"I will say to you, the House will, in fact, act," Boehner said. "We will listen to the American people, we will work with our members and we will work to protect the Constitution of the United States."

Obama, speaking at a Las Vegas high school Friday, said he took steps on his own to fix the immigration system because it's been "broken" for a long time and "everybody knows it."

Obama spent months trying to gain a House vote on a bipartisan Senate immigration bill, frustrating immigration advocates and some Democrats who wanted him to instead take action on his own. He noted Friday that 512 days have passed since the Senate passed a comprehensive bill.

"The fact that a year and a half has gone by means that time has been wasted and during that time families have been separated and during that time businesses have been harmed," he said, promising to keep working with lawmakers to achieve a comprehensive bill.

Whatever action the Republicans take will require them to balance the demands of irate conservatives without alienating moderates, Hispanics and other voters.

The other question vexing Republicans is how to undo an action set to take effect without Congress doing anything, with no obvious legislative vehicle for doing so and Obama able to veto any legislative solution they derive.

Conservative lawmakers are pushing to insert language in upcoming must-pass spending bills to block Obama's order. Party leaders warn that could lead to a government shutdown.

Numerous Republicans have discussed suing the president over his immigration orders, or expanding a lawsuit already planned over the health care law to include immigration. Yet they fret it would take too long and wouldn't have the effect of blocking Obama's orders from going into effect.

Others said that Republicans had an obligation to try to craft their own legislation. But chances of success seemed remote, at best.

In a televised address to the nation on Thursday evening, Obama defended his actions and challenged Republicans lawmakers to focus their energy not on blocking his measures but on approving long-stalled legislation to take their place.

"To those members of Congress who question my authority to make our immigration system work better, or question the wisdom of me acting where Congress has failed, I have one answer: Pass a bill," Obama said, flexing his presidential powers just two weeks after his political standing was challenged in the midterm elections.

Despite Obama's challenge to Republicans to pass a broader immigration bill, his actions and the angry Republican response could largely stamp out those prospects for the remainder of his presidency, ensuring that the contentious debate will carry on for some time.

While Obama's measures are sweeping in scope, they still leave more than half of the 11 million people living in the U.S. illegally in limbo. The president announced new deportation priorities that would compel law enforcement to focus its efforts on tracking down serious criminals and people who have recently crossed the border, while specifically placing a low priority on those who have been in the United States for more than 10 years.

Mexican President Enrique Pena Nieto applauded Obama's measures, calling them "an act of justice that values the great contributions of millions of Mexicans to the development" of the United States.

In Honduras, the office of President Juan Orlando Hernandez said Obama's decision will benefit "Honduras and tens of thousands of families."