US Republicans offered strident reaction Thursday to President Barack Obama's unilateral plan to bring millions of undocumented non-citizens out of the shadows and make them eligible for work permits.

"That's just not how our democracy works," House Speaker John Boehner said in a statement after the White House unveiled details of Obama's plan, which lifts the threat of deportation for up to five million undocumented migrants.

"The president has said before that he's 'not king' and he's 'not an emperor,' but he's sure acting like one."

House Homeland Security Committee chairman Michael McCaul branded the immigration plan "unconstitutional and a threat to our democracy."

Republicans, many of whom say any plan to legalize non-citizens who broke the law to get to the United States is "amnesty," were considering ways they might neutralize Obama's executive order.

"I will try to defund the effort for him to go it alone," warned Senator Lindsey Graham, a Republican who helped craft landmark immigration reform legislation last year that passed the Senate but failed in the Republican-run House of Representatives.

Congress must soon debate and pass spending legislation that funds government in 2015, and conservatives see the must-pass bills as potential leverage against the immigration order.

Several have argued for defunding offices responsible for issuing temporary work permits.

But the House Appropriations Committee, which oversees the budget process, indicated such action would be impossible, because the main agency tasked with implementing Obama's plan is self-funded through immigration application fees and not through the budget approved by Congress.

Texas's attorney general Greg Abbott, the border state's Republican incoming governor, wasted no time in announcing he will file a suit.

"I am prepared to immediately challenge President Obama in court, securing our state's sovereignty and guaranteeing the rule of law," he said.

Senator Rand Paul, a favorite of the Tea Party movement that opposes Obama's immigration action, urged the House to pass a resolution condemning the plan as illegal, a move that could pave the way for a court challenge.

While most Democrats are thought to support the president, he received criticism from his own ranks.

"Congress must work with the president to debate the issues and vote to secure our borders, create a tough legalization process, and ensure employers don't hire illegal immigrants," Senator Joe Manchin said.

Manchin opposed Obama's unilateral step, but said he also disagreed with the House's decision not to vote on the bipartisan reform bill that passed the Senate in June 2013.

Senate Democrat Tom Carper called Obama's effort just a "temporary Band-Aid," and that comprehensive reform can only occur through Congress.

High-profile Democrat Hillary Clinton fired off a tweet after Obama's speech, suggesting immigration will be a crunch debate topic in the next presidential campaign.

"Thanks to (Obama) for taking action on immigration in the face of inaction. Now let's turn to permanent bipartisan reform," wrote Clinton, the prospective frontrunner in the 2016 presidential race. (AFP)