John Boehner is fighting hard to right Washington’ s finances. But is he also, in effect, fighting to keep his job?

To achieve either, the speaker  of the U.S. House of Representatives has to make the budget math work. His first bid to boost government borrowing authority and cut debt was flawed in this regard. With his debt plan already under fire from the right, a low-ball CBO score was the last thing he needed.

But the Boehner Plan still looks like the likeliest path through the debt ceiling crisis. And it is a more fiscally responsible option than the Reid Plan.

Failure would show a party divided and perhaps give Tea Party Republicans reason to oust him during the next Congress. Of course, some members of his party have doubted Boehner since they recaptured the lower chamber of Congress last November. The former boss of a small business in Ohio is too much of a deal maker, these conservatives contend, not enough of a true believer.

Skepticism among the faithful increased as Boehner took the lead in negotiating with President Barack Obama. From their perspective, Boehner has come perilously close to conceding a calamitous “grand bargain” that would crack the Tea Party wing’s anti-tax platform. (But I think he’s been acting like Reagan at Reykjavik in 1986.) And his current two-step plan to raise the debt limit is far too timid for many in his caucus. Those folks still want a Cap, Cut and Balance plan, which is the best plan out there.

And it didn’t help matters when Boehner’s $1.2 trillion spending reduction turned out to save only $850 billion over ten years, according to the Congressional Budget Office. Just as damaging, the proposal is backloaded, cutting a mere $1 billion in 2012. Now Boehner has to quickly tweak the plan and hope he can lock down the 217 votes needed for passage. For the moment at least, his bill still looks to be the vehicle most able to pass the House for an eventual compromise with Senate Democrats and Obama.

Bottom line: if Boehner’s bill dies in the House, all bets are off. There’s no obvious plan B. Investors better hope Wall Street number crunchers are correct that the U.S. Treasury might have an extra week or so beyond Aug. 2 before a cash-flow crunch. (Team Geithner has pushed back against this notion.)

Speculation from one long-term Capitol Hill watcher: Boehner may then decide to jettison the tea party rump and cut a deal with Democrats and more moderate Republicans. Now I doubt such a scenario. But if that happens, he will have to start looking over shoulder at a rival more in sync with a caucus shiftingto the right. (Indeed, a new poll of tea party activists found expressed a desire for a new House speaker.)

Republicans think the current fiscal conflict may pale next to a coming war over taxes and spending after the 2012 presidential election. But will Boehner still be one of the generals? It may depend on the fate of the Boehner Plan.