How do you expect to spend your July 10? In staff meetings? Kicking it at the beach? Digging out from the Fourth of July holiday backlog?

Whatever your plans, they’re likely to be way more fun than the way John Boehner and his fellow House majority leaders anticipate passing their day: namely, listening to their colleagues rant and rage about immigration at a specially organized conference gripe session on the topic.

The closed-door powwow promises to be an electrifying exercise in spleen venting, thrust upon them by their Senate brethren. At some point in the next day or two, the upper chamber is expected to pass its sprawling, blood-sweat-and-tears-drenched overhaul of our FUBAR immigration system. In the run-up to voting, Hill watchers have been aflutter over whether the bill can pull enough Republican support to hit 70 “yeas”—maybe even 71! A procedural test vote Monday topped out at a mildly disappointing 67 (including 15 R’s). But the last-minute horse trading continues, and reform advocates remain optimistic that the final tally will be big and bipartisan enough to goose the House into passing something similarly sweeping.

Except ... when a policy area as complex and crazy-making as immigration collides with a House majority as fractious, divided, and obstructionist as this one, there is only so far momentum can take you. Already, House leadership is clear that it has no intention of taking up anything remotely resembling the wide-ranging Senate bill, with its path to citizenship and lack of hard targets for border apprehensions. No way. No how. It couldn’t even if it wanted to, says one Republican aide. “If we tried, it would probably fail.”

Everyone pretty much agrees that the House will essentially ignore the Senate’s work and put forth a wholly different bill, or, more precisely, a series of four narrowly tailored bills focused on individual policy pieces that the House deems important (read: border enforcement). Then you “wrap those together,” says the aide, and it’s off to a joint conference with the Senate. “In conference,” observes GOP leadership staffer turned strategist John Feehery, “anything goes.”

But to get even that far, the House first needs to pass something. “How they get this done is a matter of great speculation,” says Feehery. “It’s hard to pass anything out of the House.”

What about the 70-vote, big-mo shaming strategy?

Don’t put too much stock in it, advises Rep. Tom Cole, whose deputy-whip duties put him in the thick of the House vote counting. A 70-plus win in the Senate would prove marginally helpful at best, he asserts, and adds that the composition of Republican support there would matter more than the raw numbers. “If they can start moving guys who are well-identified conservatives” on the issue, that could make a difference, says Cole. Otherwise, “why in the world would a majority of House Republicans, who are on average more conservative than Republican senators, listen to a minority of Republican senators?”

Beyond individual ideology, the politics are simply far trickier for House members, reminds Cole. “Remember, roughly two out of three senators will not be running next time. Everybody in the House will be on the ballot. And, as a rule, they represent more homogenous districts than senators, who represent entire states.” Add in the fact that the midterm electorate tends to be whiter, older, and more conservative than in presidential years, and even House Republicans who might approve of the Senate plan on the merits have ample political incentives to run screaming from it.

Cole and Feehery both note that the Senate vote is likely to impact House members on a delegation-by-delegation basis. General momentum is all well and good, Cole explains, but “what matters more to individual members is how their senators voted.” A “yea” from their state’s Republican senator (think: Rubio in Florida) or senators (Alexander and Corker in Tennessee; Flake and McCain in Arizona) could provide at least a bit of political cover. Feehery agrees: “It makes it easier when members can say, ‘My home-state senators voted for it.’”

This is not to suggest that reform won’t happen. House Republican leaders are highly motivated to lance this boil. “This is going to be an issue that Democrats use to beat up Republicans until it’s taken off the table,” acknowledges Cole.

And although much has been made of Boehner assuring his conference that he will abide by the so-called Hastert Rule on immigration (meaning that he won’t move a bill that doesn’t have the support of a majority of the majority), Hill veterans note that there are ways around this unofficial mandate.

In some cases, leadership can get a majority of its members to express private support for a bill even when they’re unwilling to vote for it, notes Feehery. (Cole cites the fiscal-cliff deal as an example.) As for the official vote count, Republican staffers are already allowing for a bit of wiggle room. While passing legislation with more D’s than R’s would be a no-no, passing it with, say, 120 votes from each team would be just fine. Of the Hastert Rule hubbub, the GOP aide says, “It’s kind of a lot of ado about nothing.”

Or as Cole puts it, “The Hastert Rule is a rule except when it’s not.”

Just don’t talk that way in front of the conference’s right wing. They already have issues with the leadership, and some have even launched a crusade to make the Hastert Rule binding. (As if the House needed any more hurdles to getting stuff done.) All of which suggests that Boehner et al should rest up over the recess and brace for a July 10 “listening session” that will, by comparison, make their last colonoscopy seem like a week in Palm Beach.