With only days to go before a deadline for funding the Department of Homeland Security, Senate Majority Leader Mitch McConnell is desperately seeking a way to sell Republicans in both houses of Congress on a plan to get themselves out of the trap that President Obama set for them. His conservative critics aren’t wrong when they say this is nothing more than a GOP surrender that gives up any hope of taking a stand against the president’s extralegal executive orders granting wholesale amnesty to up to five million illegal immigrants. But unless McConnell can persuade House Republicans to go along with him, the understandable desire to defund those parts of the government that will carry out the president’s orders will cause the party to embark on another suicide charge that might prove to be even more disastrous than the 2013 government shutdown.

Let’s specify that Tea Partiers and other GOP stalwarts are right to be outraged about the president’s end-run around the Constitution. The notion that a president has the right to legislate on his own simply because he says he gave Congress time to do what he wanted it to do and must now act since they failed to is absurd as well as reflecting contempt for the rule of law. Regardless of one’s views about the need for immigration reform, the president’s actions constitute an ominous precedent that presage a constitutional crisis as the executive branch runs roughshod over the normal order of government. Indeed, even many Democrats said as much last fall prior to the orders, especially those up for reelection.

But simply because something is wrong and should be stopped doesn’t necessarily mean there is a way to do it that is politically palatable. The orders were given in a way that there is no option for halting their implementation other than defunding the Immigration and Naturalization Service, which now falls under the purview of the Department of Homeland Security. The courts may rule in favor of the 26 states that have sued to halt Obama’s orders. The decision of one federal judge in Texas in favor of that suit has, at least temporarily, stopped Obama in his tracks. But unless that track works—and it is likely that it won’t—the only alternative is defunding DHS.

It is true that Republicans are attempting to keep the rest of Homeland Security operating while preventing INS from doing the president’s will with respect to amnesty. But with Democrats in the Senate filibustering that effort and the president ready to veto that measure even if the Upper Chamber’s minority doesn’t hold on, taking a stand on illegal immigration will shut down the entire department.

While most Americans don’t like the idea of government shutdowns under any circumstances, furloughs for DHS employees right now is about the worst political idea anyone in Washington could come up with. The GOP could probably get away with shutting down the Department of Education or Housing or Health, Education, and Welfare or any number of other federal bureaucracies and not be hurt by it. But defunding DHS at a time of rising concern about terrorism is a political loser as well as arguably very bad policy. It not only creates another liberal narrative about Republican obstructionists trying to stop the government from operating. It also allows the president to change the subject from his lack of a coherent strategy to defeat ISIS to the old tried-and-true meme about Republicans blowing up the government.

Conservatives are right that this isn’t fair. A principled stand by the GOP against Obama’s executive orders isn’t anymore extremist than the Democrats’ refusal to compromise or step back from amnesty. The assumption that Republicans should be blamed for a shutdown is based on biased media reporting that reflects Democratic talking points. Unfortunately, the public seems to have bought it, in no small measure because the GOP’s small-government philosophy seems to make it more likely to act as if the government does deserve to be blown up.

But fair or unfair, it is a matter of political reality. As even Senator Marco Rubio noted today, shutting down DHS is simply unthinkable right now. Thus, the GOP should swallow hard and follow McConnell’s plan by passing a “clean” funding bill for DHS and then having a separate vote on a measure to stop the executive orders that will inevitably fail. If the House balks, it won’t matter that President Obama and the Democrats deserve the lion’s share of the blame for starting the fight with the orders and then filibustering a GOP bill to fund DHS.

Such an outcome is frustrating for party activists that turned out and elected a Republican Senate as well as a GOP-run House. But as infuriating as it may be, they need to realize that the only way to rescind those orders is going to mean electing a Republican president of the United States. And that is a prospect that will be less likely if they wind up shutting down DHS and further damaging their brand as a party at time when they should be gaining ground at the Democrats’ expense on foreign policy.