The question is: How far can it go?
Immigration might be the single biggest source of strain between two powerful factions of the Republican coalition — the big-business wing and the conservative grassroots.
Handled poorly, the issue could split the party. Any move too far to one side risks turning off the other.
So Republicans are seeking a response that lies between shutdown and climbdown — an option that falls on a continuum somewhere between stalling the federal government and completely capitulating to the commander-in-chief.
One day after Obama offered a three-year stay to nearly five million undocumented immigrants, Republicans hadn't quite figured out their next move.
"We're working with our members and looking at the options that are available to us," John Boehner, the top Republican in the House, said Friday.
"But I will say to you that the House will, in fact, act."
Easier said than done.
The range of potential responses is as vast as the variety of views on immigration policy in the Republican caucus, where some members want all-out political war with Obama and others share his views on immigration.
In fact, a Pew Center study this year found a far bigger cleavage on that issue than other major ones that split the party's main factions — including gay rights, military intervention, and the role of Wall Street.
The study found a whopping 52-per-cent divergence in response to the statement, "Immigrants today are a burden because they take jobs, housing, health care." A mere 21 per cent of self-described "business conservatives" agreed with that statement — compared with 73 per cent of "steadfast conservatives."
One thing that unites them is disdain for the president.
They've managed to rally around the idea that he overstepped his authority this week. They say Obama had no constitutional right to promise parents of U.S. citizens that they could register to stay in the country, and work, for three years.
Even Jeb Bush, a potential centrist candidate for the presidency in 2016 and the softest of the Republican softies on immigration, posted a Facebook statement denouncing Obama's announcement as an "ill-advised unilateral action."
Many of the comments below it contained too many naughty words to print — from Republican voters, directed at Bush. Some of the conservatives commenting on Bush's Facebook page wanted more: they wanted to impeach Obama.
That's the kind of anger in the ranks that Boehner and company will be contending with over the next few weeks as they prepare a response for the new Congress after the holidays.
The brass will be getting pushed by more hawkish members like Sen. Ted Cruz, who penned an op-ed Friday that laid out two preferred responses. One, stop confirming all of Obama's appointments to the courts, executive agencies, and embassies until he backs down; Two, stick an anti-deferral clause into every spending bill and dare Obama to shut down the government.
"If he acts by executive diktat, President Obama will not be acting as a president, he will be acting as a monarch," Cruz wrote in Politico.
"Thankfully, the framers of our Constitution, wary of the dangers of monarchy, gave the Congress tools to rein in abuses of power. They believed if the president wants to change the law, he cannot act alone; he must work with Congress."
The pulse of the party could be heard on right-wing radio.
One host, Mark Levin, was comparing the president to a fascist, calling him "Benito Obama." Rush Limbaugh sounded incredulous Friday that the party brass was trying to calm the base, instead of fighting the president.
Another potential 2016 candidate suggested a long-term legal strategy.
Sen. Rand Paul said Congress should start by immediately passing a non-binding resolution — one that simply states that Obama's action is contrary to the will of the elected body.
That's because the Supreme Court decided over a half-century ago that executive actions by presidents are limited, and can be struck down in court if they're found to contradict the clear will of Congress.
"What I would recommend to the House is, they should immediately pass at least a resolution saying that what he is doing is contrary to the will of the House of Representatives," Paul said on Fox News.
"History will treat him unkindly on this if he thinks he can become king."