The odds have crested the 50-50 threshold for what would surely become one of the year’s biggest legislative achievements — an overhaul of how doctors and other Medicare providers get paid. And the usual encrusted ideological positioning, at both ends of the political spectrum, is no longer the biggest obstacle.

Instead, what’s standing in the way is a springtime functionality gap between the Capitol’s two wings.

The House is on course Thursday to embrace something resembling a legislative unicorn: A bipartisan plan to restrain entitlement spending. Both Speaker John A. Boehner and Minority Leader Nancy Pelosi claim pride of authorship in this modest breakthrough of a bill, and they’re basking in the expectation it will pass with the votes of most Republicans and most Democrats.

It’s a phenomenon rarer on the Hill than flurries at the end of March. The Hastert Rule (measures coming to the House floor must command support from a majority of the GOP majority) is going to co-exist with what might be called the Peterson Reality (you can count on one hand the number of remaining Democrats who are like Minnesota’s Collin C. Peterson, whose reliably “red” districts give them a political survival motive for going along with the GOP).

But there’s deepening suspense to see whether the Senate will take the House’s loud “Yes!” for an answer.

If senators decide to acquiesce to the House plan, they’ll probably do so in the form of a lickety-split voice vote at the last minute before their spring break starts Friday night. That’s the senatorial equivalent of an, “Oh, I guess that’s OK …” Don’t expect triumphant speeches, congratulatory news conferences or even a call of the roll.

The time pressure comes from next week’s deadline — the current Medicare payment formula lapses on March 31. Unless Congress replaces the existing rules or extends the status quo, in April physicians will see a 21 percent cut to their reimbursements for treating the elderly. In an almost annual ritual known as the “doc fix,” Congress has stepped in 17 times previously with legislation temporarily forestalling such reductions, part of a deficit-reduction law enacted almost two decades ago.

But there are solid reasons, both tactical and petty, why the Senate will either deadlock over or proactively postpone the “permanent doc fix” measure — perhaps only for a month or so, but maybe until later this year or beyond. (If that happens, the get-out-of-town votes at the end of the week will be to apply an 18th consecutive patch to the formula.)

Senate Majority Leader Mitch McConnell has been pledging since election night to do whatever he can to revive the Senate’s traditional deliberative culture, and working to dragoon all his colleagues into an immediate acceptance of the House’s work product would openly contradict those “return to regular order” promises.

Beyond that, the Kentuckian’s experience as a strategic thinker may have given him another idea: Such a rare bipartisan agreement should not be permitted to become law so easily; instead, such a “unicorn” is best consigned to the stables until his fellow Republicans have readied some more politically complicated freight to catch a ride on its back.

It’s also the case that, if the Boehner-Pelosi pact sails through, it will unavoidably cast additional unflattering light on the sour relations between McConnell and Minority Leader Harry Reid, who can hardly agree these days on when the Senate should schedule an hour off for lunch.

If McConnell doesn’t raise a hand against the bill, there’s a chance the Democrats on the Senate Finance Committee will be the ones to put a hold on it — not because they’re unalterably opposed to the package, but because they are peeved at not being consulted on the deal.

And, as even a modestly cynical observer would note, perpetuating the “doc fix” debate assures a continued steady flow of generous campaign contributions to lawmakers in both parties — from their rich physician constituents as well as the political arms of an enormous array of medical specialty groups.

Enacting the Boehner-Pelosi plan would not only turn off that spigot, but also transform the world of health industry lobbying by allowing doctors to count on regular inflationary increases in their Medicare fees and obviating the need for any more temporary patches.

To make most Republicans happy, it would accomplish this without raising taxes. Instead, it would offset about a third of the $210 billion cost during the next decade, mostly by making wealthier beneficiaries pay more for their coverage but also from trimming some payments to hospitals. To make most Democrats happy, the bill would also extend for two years the Children’s Health Insurance Program, which covers the medical expenses of poor kids. Hoping to plump up support in both parties, and woo senators as well, the package also extends programs that pay for therapy services, subsidize ambulance systems, keep community clinics open and prop up the books of rural hospitals.

The most conservative Republicans object on the grounds that the deficit should not be permitted to grow by $140 billion for almost any reason, including preserving the current levels of physician income. Others on the right don’t want to ask elderly rich people to pay more for their Medicare.

The most liberal Democrats oppose the package for not giving CHIP a longer lease on life, and leading abortion-rights lawmakers lament the deal would maintain the current rules preventing spending on abortions except in cases of rape or incest.

More often than many realize, senators live up to the stereotype that their egos are both bigger and more easily bruised than those of their House counterparts, and that the same goes for their turf consciousness, fundraising ferocity, hostage-taking zeal and proclivity to play it too clever by half. All of that is in play in the next three days.

Related:

Make-or-Break Week for Republicans on ‘Doc Fix,’ Budget

McConnell Plots a Functional, Bipartisan Senate

Quiet Win for Boehner? Bending the Entitlement Curve

Republicans Open to Potential ‘Doc Fix’ Deal

Conservatives Still Fuming Over Secret ‘Doc Fix’ Vote

The 114th: CQ Roll Call’s Guide to the New Congress

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