An ocean of figures fill the final fiscal blueprint Paul D. Ryan will unveil as chairman of the House Budget Committee. But the number that matters most never appears: 16.  

That’s the maximum number of Republicans who can turn their back on the budget resolution when it comes before the full House next week without dooming the caucus and its most nationally prominent figure to an embarrassing election year failure.  

Why the Wisconsinite and his leadership wingmen are pressing ahead with this seemingly high-risk, not-very-high reward venture remains confusing to many in the party, and the GOP conference divided sharply last week on whether a budget should even be unveiled. But ultimately these four arguments won out:

• Making some bold proactive policymaking ideas will refute the criticism of the GOP as a chorus eager to shout “no” at whatever President Barack Obama does or says, but unwilling to come up with any alternative vision.
• The House majority is obliged to write a budget given how critical it remains of the Democrats in charge of the Senate. The GOP says the Democrats are “shirking their responsibility” by opting against drafting a companion measure for the fourth time in five years.
• Ryan’s plan has many more elements that will rally the Republican base than will make those voters agitated or dispirited. Its call for balancing the federal books in a decade with dramatic cuts to entitlement spending, an end to Obamacare and no new taxes at least has the potential to unify the establishment and tea party factions. Its willingness to spend 3 percent more on domestic programs than the sequester would have allowed next year will infuriate only a relatively small number from the small government crowd.
• Years of experience has shown Democrats are unable to get significant political traction (outside their own base) from their assaults on the budget as a sop to the rich, a reward for special interests and an assault on the elderly. Putting Ryan, the personification of GOP fiscal policy, on the national ticket in 2012 was hardly a drag on Mitt Romney’s candidacy; he still won a majority of older voters, independents and those who listed either the economy or deficit as the top problem facing the country.

In other words, House GOP leaders have concluded they don’t have a lot to lose from budget debate, and that it actually has the potential to burnish the party’s campaign season image of conservatism and responsibility.  

That theory won’t be tested much Wednesday. Ryan is confident he will withstand the initial wave of vituperative criticism from the Democrats, repel their initial onslaught of amendments to remake or undermine his plans and advance his budget on a party-line vote of his own committee.  

The suspense will come just before Congress decamps for its two-week spring recess. Because three seats are vacant, it will take only 217 votes to assure victory on the floor. But because no Democrat is going to come close to pressing the green “yes” button, Ryan can only afford 16 defectors. (There were 10 last time around.)  

This year, Ryan has a minimal margin for error, especially in this context: Four times as many GOP members — 62, to be exact — voted in December against the bipartisan budget accord hailed by their leadership after it was unveiled by the Wisconsin Republican and his Democratic counterpart, Senate Budget Chairwoman Patty Murray of Washington. The conservative Republican dissenters balked at the central feature of the deal, allowing the cap on discretionary spending to rise from the sequester’s $986 billion to $1.012 trillion in the current year and $2 billion more than that next year.  

That $1.014 trillion top line for fiscal 2015 is reiterated in Ryan’s budget. But during the decade after that, he envisions boosting defense spending by half a trillion dollars but taking about $50 billion annually from non-defense programs — a shift in national priorities clearly designed to win back the votes of many of the budget hawks who opposed the Ryan-Murray deal.  

So, too, are the budget’s other big-ticket proposals for savings, which would fundamentally alter almost every part of the social safety net during the next 10 years net: cutting $2 trillion by wiping away the Affordable Care Act; cutting more than $1 trillion from food stamps, college grants, farm subsidies and federal pensions; cutting $700 billion from Medicaid; turning Medicare for people now younger than their mid 50s from an open-ended entitlement into a fixed-price subsidy. (Social Security would be left alone, because while the Republicans may want to appear bold, they don’t want to act reckless.)  

None of those ideas is going to become law in 2014, but each of them might win over a few GOP votes this month.  

One pivotal group to watch is the nine Republicans hoping they’ll be part of a Senate GOP majority  come 2015: open-seat favorites Shelley Moore Capito of West Virginia and James Lankford of Oklahoma; incumbent challengers Tom Cotton of Arkansas, Steve Daines of Montana, Cory Gardner of Colorado and Bill Cassidy of Louisiana; and the trio bidding for Georgia’s open seat: Paul Broun, Phil Gingrey and Jack Kingston.  

Cotton, Daines, Gardner, Broun and Kingston voted “no” in December. If they change course, that will signal that candidates in hot races are willing to shoulder the “out of the mainstream label” now in the belief they’ll be rewarded later. And it will mean Ryan’s budget stands a shot at actually winning adoption in the House, where it will be remembered as a manifesto for governance whenever the GOP next controls all the levers of legislative power.