PASS A CLEAN BILL. This is the option preferred by congressional Democrats who have been resolute in saying they won't support anything else. With Democratic support in the House and Senate, it seems likely that a clean bill can pass both chambers and earn the president's signature.
But the consequences of pursuing such a strategy for Boehner, and to a lesser extent McConnell, could be severe. Both leaders urged conservatives to hold their fire over the president's executive action on immigration at the end of last year, telling members that they'd have their chance when the DHS bill came up early in this Congress.
Another concession, and no action on what conservatives term Obama's "unconstitutional executive amnesty," could lead to an insurrection in the Republican ranks in both chambers.
SHUT IT DOWN. Both parties believe the other will earn the blame if DHS shuts down at the end of the month. But that isn't a risk leadership in either chamber—and the vast majority of members—wants to take.
The optics, most agree, of shutting down the department in the midst of the U.S. fight against ISIS and cybersecurity breaches, aren't ideal. Boehner and McConnell have both said they won't allow that to happen.
Senate Democrats say they want to avoid a shutdown as well, but also want to protect Obama from effectively shuttering DHS with his veto pen.
"We have no choice," Schumer said of Democrats' repeated filibuster over the DHS bill. "Because if the bill were to pass, be debated and passed, the president would veto it and [part of] the government would shut down. So we are not letting that happen."
Regardless of who would get blamed for a shutdown, eventually Congress would have to pass legislation to end it. And barring a complete cave by Democrats, Republicans would have the same menu of bad options.
FORCE THE HOUSE TO SEND A NEW BILL. The weeklong effort to overcome the Democratic filibuster arms McConnell with an example for House Republicans of his body's limitations.
"The magic number is 60 in the Senate and 218 in the House," says Thune. "They realize we have fought the good fight over here. This is the third cloture vote and we haven't been able to break any Democrats off. At some point, something has to give."
Yet, many senators say their hands are tied. They cannot break the Democratic filibuster, but because the DHS bill is a funding bill, senators argued at their lunch on Thursday that it's unconstitutional for them to draft their own legislation. They need the House to try again.
That would conveniently take the pressure off Senate Republicans. The spotlight would turn again to Boehner as he finds new, passable language for a funding bill, faces his conference for a vote, and volleys it back across Capitol Hill before the deadline.
Boehner doesn't seem to have much of an appetite to begin his part of the game again from scratch.
"The House fought this fight. We won this fight. Now it's time for Senate Democrats to work with Senate Republicans to stop the president's unilateral actions with regard to immigration," Boehner said.
Daniel Newhauser contributed to this article