While House Republican leaders are waiting for the Senate to restore funding to Obamacare in the stopgap spending bill, they are also refining their approach to the second fiscal showdown of the fall — over the debt limit.

Regardless of whether GOP conservatives and President Barack Obama reach a deal that averts a partial government shutdown in eight days, the Treasury will need permission from Congress to borrow more money as soon as the fourth week of October. And already it’s becoming clear that neither side is going to be more flexible on what to do about that than it has been on the continuing resolution.

The phone call Obama and Speaker John A. Boehner had late Friday was all about the debt ceiling, not the spending impasse, and lasted only a couple of minutes. The president declared he would not make any sort of policy concession in return for a higher legal borrowing limit, and the House leader made it clear his side would insist on just such a trade-off.

What the GOP might propose became more clear late last week, when leaders outlined not only a delay in implementation of the 2010 health care law — a more comprehensive attack on the statute than the defunding language in the CR — but also several other budget policy proposals most congressional Democrats oppose. That includes reducing some Medicare benefits for the more affluent elderly, changing the government’s inflation calculations to so-called chained CPI to curb the growth of Social Security cost-of-living increases, setting in motion a revenue-neutral overhaul of the tax code and requiring the immediate permitting of the Keystone XL oil pipeline.

The one sweetener the preliminary Republican plan would envision is that, in return for achieving so many of its policy goals, the GOP would be willing to take the debt ceiling off the congressional agenda until after the midterm elections. The legislation being drafted would not set a new monetary limit on borrowing (It’s now $16.7 trillion) but instead would permit the Treasury borrow whatever it needed until the third week of November 2014.

The package would be theoretically true to the formula that Boehner has been talking about for two years — that every dollar in new borrowing should be matched by an equivalent amount of spending reduction — and so would have a high probability of getting through the House with the support of almost every Republican. (A few will object to using a date instead of a dollar amount for the debt limit increase.)

But there is no reason to believe this approach would have any more chance of success in the Senate than the defund-Obamacare CR now being prepared for evisceration by the Democrats. And Obama’s rhetoric about not being taken hostage or made a victim of extortion has given him little room to consider the House GOP’s approach.

What the GOP is hoping, of course, is that they will be able to successfully portray the president’s intransigence as the reason the government is edging toward a default and risking another wave of Wall Street anxiety.

What the Democrats are hoping is that the GOP will realize its gambit isn’t working in enough of time to prevent a market stumble or crash.