With the debate over immigration in America locked in a stalemate, it would seem neither side has much to fight for. And yet both sides are fighting furiously—in Congress, in the courts, and in the political arena.

The slow death of the legislative process in the House and the Republican takeover of the Senate have killed any hopes for passage of a big reform bill in the foreseeable future—a victory for the proposal’s opponents. On the other hand, President Obama in November used executive action to temporarily protect as many as 5 million undocumented immigrants from the threat of deportation—a major, long-delayed victory for immigrant-rights advocates.

Proponents and opponents of reform have reached the limits of what they can achieve on their own, and are dissatisfied with the status quo, but none of them can change it independently, and they’re not prepared to compromise.

In Iowa this weekend, top Republican presidential contenders assembled at a “Freedom Summit” convened by Representative Steve King, the right-wing congressman who is a high-profile opponent of illegal immigration. You may recall the time he sought to replace the popular image of immigrant children as hardworking strivers with the idea that many have “calves the size of cantaloupes” from “hauling … marijuana across the desert”; last week, King excoriated First Lady Michelle Obama for inviting, as a guest to the State of the Union, “a deportable”—Ana Zamora, a 20-year-old Dallas college student brought to the U.S. as a toddler by her undocumented Mexican parents.

Potential candidates Chris Christie, Ted Cruz, Ben Carson, Mike Huckabee, Rick Perry, Rick Santorum, and Scott Walker all spoke at King’s Iowa gathering; other top contenders, including Jeb Bush, Marco Rubio, Mitt Romney, and Rand Paul, did not attend. The Republicans were met in Iowa by a phalanx of immigration activists and Democratic officials, including the chairwoman of the Democratic National Committee, who loudly decried their willingness to kiss the ring of such a divisive figure. King has become notorious in the Hispanic community, but it’s not clear how much clout he will have in the 2016 Iowa caucuses: Though thought to have a following among hard-core conservatives, he made no endorsement in 2012, and in 2008 endorsed the television actor and former senator Fred Thompson, who finished third.

“I hope this is not wishful thinking—I think Steve King is in the process of marginalizing himself, even within his own party,” said Harold Heie, an immigrants’ rights advocate based in Sioux City, whose group sponsored a pro-immigration-reform ad in the Des Moines Register. Failing that, said Erika Andiola, co-director of the DRM Action Coalition, Republicans need to remember what happened in 2012, when Romney’s loss was ascribed in part to his poor showing among Hispanic voters. “It’s very important to get that message to the presidential candidates—to remind them what happened to Mitt Romney and remind them what the Latino community’s really thinking,” she said.

Meanwhile, in Congress, Republicans have vowed not to take Obama’s executive immigration actions lying down. In December, they passed legislation to fund the whole government for the better part of the year—except for the Department of Homeland Security, whose purview includes immigration enforcement, which was funded only until next month. The idea was that this would give the new Republican Congress a chance to impose some sort of restriction on Obama’s immigration policy. But it’s never been clear how they planned to do this. Earlier this month, the House passed a measure seeking to invalidate the executive actions, but it’s not expected to get through the Senate, and Obama has said he would veto it. Republican House and Senate aides have confirmed to me that there was no advance game plan for the DHS gambit; leadership seems to be hoping that the right-wingers will exhaust themselves as they try and figure out something to do, and finally accept that they must suck it up and fund the department or be accused of putting American security at risk. The alternative, a department shutdown, would be bad politics, particularly in light of the recent terrorist attack in France.

Obama’s unilateral liberalization of immigration policy won’t begin to go into effect until the end of next month. Advocacy groups are gearing up for a major enrollment push, for reasons both substantive and symbolic. Though the relief from deportation is only temporary, such an assurance can make a huge difference in the lives of the undocumented, they say, while demonstrating the appetite and enthusiasm for the measure will put pressure on policymakers to go further. Opponents, meanwhile, have pinned their hopes on a lawsuit, brought by 24 states, that challenges the action in federal court. Hearings were held on the suit earlier this month in Brownsville, Texas, before a conservative judge thought to be sympathetic to the states. On Friday, a group of prominent mayors fired back with a court brief siding with the administration. “We believe we have a moral obligation to act—to answer the lawsuit with the voices of the grassroots,” New York City Mayor Bill de Blasio said at a Washington press conference with other mayors announcing the brief. He said he was speaking on behalf of “12 million people who are not yet documented but are still our constituents.” The Texas judge is expected to decide soon whether to temporarily halt the deportation-relief measures while the lawsuit proceeds.

The upshot of all this action is a lot of furious argument over a policy in relative stasis. Republicans are expected to control all or part of Congress many years into the future, and their demonstrated unwillingness to reform immigration continues to be a political problem for the party’s national candidates, even as they appear mostly powerless to stop the president from allowing millions of immigrants who came here illegally to live and work openly in the United States. In his State of the Union last week, Obama raised immigration only to say that  he hoped his opponents would leave his policies alone. “We can’t put the security of families at risk by … refighting past battles on immigration when we’ve got a system to fix,” he said, adding that he would veto any bill that sought to do so. Advocates are mostly pleased with what the president has done, though some are still pressuring the White House to do more; at the same time, they have little hope for a permanent solution and are at a loss to regroup and go forward. Still, for the millions of undocumented immigrants, their families, and those who advocate for their interests, giving up isn’t an option, notes Frank Sharry, director of the immigration-reform group America’s Voice. “Some of us are lifers, I’m afraid,” he said.