An alternative House Republican tactic for holding the government hostage in the crusade to hobble Obamacare has come into sharper focus today. It doesn’t look to have any better chance of  success than the first idea floated this week, but the consequences of pursuing the second course could be much more dramatic.

Majority Leader Eric Cantor, R-Va., is floating the idea of insisting on a one-year delay in implementing the health care overhaul, or at least its individual mandate, as the price for legislation to increase the federal debt limit, which will hit its ceiling sometime in mid-October or early November.

Many conservatives and junior members embraced the debt-ceiling approach at a GOP caucus meeting Tuesday, and only a handful of veterans and politically vulnerable members expressed reservations — a reaction prompting the leadership to retain the economically risk-filled strategy as an option for a climactic confrontation in this fall’s budget wars.

The previous notion was to advance legislation with the same delaying effect, but tying it to a catch-all spending bill to keep the government running past Sept. 30 to at least Dec. 15. The GOP’s confrontational right flank expressed deep disappointment at that approach when it was unveiled Tuesday. It would permit the Senate Democratic majority to reject the anti-Obamacare provisions with a quick roll call and then send the $986 billion continuing resolution to the president for his signature.

Whether the conservative rebellion becomes intense enough to block this legislative two-step may be known by the end of the day — the House is supposed to debate the CR on Thursday.

If House Republicans acquiesce, concluding that holding their fire against the health law is preferable to provoking a government shutdown, that will only intensify the conservative clamor to embrace Cantor’s idea of making an Obamacare delay the ransom for increasing the Treasury’s borrowing authority. According to a new report out Tuesday, Treasury will need action no later than Nov. 5, and maybe as soon as Oct. 18,  in order to prevent a cataclysmic government default on paying back its bonds and other debt instruments.

But such a trade off would get only a handful of Democratic votes in the House, has almost no chance of surviving in the Senate and would be assured of opposition from President Barack Obama, who to this point has said he will countenance no conditions at all on increasing the permissible debt limit above $16.7 trillion.

The Bipartisan Policy Center, a Washington think-tank that estimated the default deadlines, also projected that the government would need to borrow $1.1 trillion more than that between now and the 2014 midterm elections.

Every round of drama over whether the government will cover it debts on time has the potential to cause significant economic distress. But the emerging consensus among House Republicans this week is that their political self-interest tells them to be less concerned about the financial markets’ anxieties next month than they are about the voters’ worries this month.