A four-day weekend for the House is affording GOP leaders extra time to go over the long list of lessons they were retaught by the farm bill’s catatonic collapse.

Perhaps the most obvious and the most important among them: If you’ve got the votes, then vote. If you don’t, bide your time. But be sure you can count well enough to know the difference.

Forgetting this one lesson next time, on the immigration bill, will almost surely prove fatal to the most sweeping domestic policy overhaul of this decade. It will very likely lead to the dismissal of all three men at the helm of the majority caucus. And it could well poison the Republican Party for years in the eyes of the nation’s fastest-expanding demographic group.

For GOP leadership, the importance of separating their external challenges from their own shortcomings — and focusing on what’s within their power to fix — cannot be overstated before an immigration debate is scheduled.

The farm bill’s defeat showed Speaker John A. Boehner’s leadership in need of a course in remedial congressional math. Republicans bemoaned the fact that Democrats delivered only 24 votes after promising at least 40. But even if those extra 16 votes had ended up in the “yes” column, the legislation still would have fallen short. GOP leaders would have had to switch four of their own from “no” to “yes” to eke out a no-votes-to-spare victory.

Beyond that, Boehner and his frenemy deputy, Majority Leader Eric Cantor, ought to have been able to figure out that engineering the adoption of not one but two conservative amendments in the final hour — in hopes of plumping up GOP support for the bill — was a gamble that would drive away a more-than-offsetting bloc of Democrats.

And if they didn’t understand that, the genial former staffer, Majority Whip Kevin McCarthy, should have had reams of whip counts at the ready to tell them the risk vs. reward: How many new Republicans would be brought aboard by the “dairy reform” language? How many Democrats would be lost? What about requiring more work from food stamp recipients: Would that add more Rs on final passage than the number of Ds who would peel away?

For generations, these have been precisely answerable questions for House leadership organizations of both parties. It was absolutely true of the formidable whip team that Tom DeLay put together for the resurgent GOP majority of the late 1990s, when Boehner made his debut in the command structure as Republican Conference chairman. DeLay rarely lost, and so often won by the skin of his teeth, because he knew just when it was safe to bring “the hammer” down.

The same was true of the Democratic majority whip team in the last decade. For two years it was able to tell Boehner, as minority leader, just how many votes his side would need to come up with to advance Bush administration proposals in their mutual interest. For two years after that, it advanced the Obama agenda without incident by gauging precisely how many Blue Dog-types were joining virtually all the Republicans in walking away.

Many, many things are different for today’s House Republican majority. Its ideological fracture — between the very conservative and the really, really conservative — is as profound as ever. Nine out of 10 have reason to fear a primary fight more than the general election, which means they’re more beholden to the Club for Growth and Heritage Action than to their own leaders.

Almost half arrived since January 2011, meaning they know nothing of life in the minority and very little about the ways of the past. And, because so many were propelled toward the Capitol on an anti-establishment wave, they have little interest in such venerable political virtues as party loyalty and teamwork in the pursuit of shared strategy.

The dissolution of the old order is so profound that an astonishing six committee chairmen were among the 62 Republicans who voted to defeat the farm bill: Jeb Hensarling of Financial Services, Ed Royce of Foreign Affairs, Bill Shuster of Transportation and Infrastructure, Jeff Miller of Veterans’ Affairs, Robert W. Goodlatte of Judiciary (a former Agriculture chairman, to boot) and  — most amazingly of all — Paul D. Ryan of the Budget Committee. He looks for all the world to be seriously weighing whether he’d rather run for president in 2016 or make leading the House his political life’s ambition.

Ryan presumably concluded both potential goals were best served by siding with the conservative hard-liners. A strong argument could be made that he was wrong and that someone aspiring to the top job needs to display a willingness on tough votes to show his colleagues that sometimes followership in an essential component of leadership.

All those are limitations to leadership that may be beyond the control of Boehner or whoever his successor might be, whether that person is installed before the end of the 113th Congress or after.

But the Boehner-Cantor-McCarthy triumvirate ought to be able to get a better handle on the challenges they are up against. And they will have to do so if they have any hope of engineering passage of some sort of immigration bill — whether it’s this summer or later and whether it’s mostly with Democratic votes or with a majority of their GOP majority. The latter “Hastert rule” formula has a much longer shot at success even though Boehner (for now) insists he’s insisting on it.

That means GOP leaders getting beyond last week’s vituperative finger-pointing at their Democratic counterparts, swallowing some pride and enlisting their help in avoiding another “major amateur hour,” as Nancy Pelosi labeled it. McCarthy might start by admitting he’s overdue in asking just how many House Democrats would vote for the bill the Senate’s going to be passing this week.

And then he can turn his attention to his own side. DeLay turned whip counts into an exact science with his relentless push for candor from his colleagues. He wanted to know whether each member was with him or against him, and he’d keep asking until he was sure of the answer. “Yes” was best, of course, but a hard “no” was preferable to a squishy “probably.”

That shouldn’t be such a heavy lift in a place where “Your most valuable asset is your word” remains a cliché that most Republicans still use with apparent sincerity.