House Speaker John Boehner (R) and Minority Leader Eric Cantor (R) just announced that Republicans will, once again, seek to attach Obamacare-related provisions to the continuing resolution that would keep the federal government open after today. Earlier this afternoon, the Senate stripped out Obamacare provisions and sent the bill back to the House.

Boehner and Cantor have two new demands they want to attach: a one-year delay of the individual mandate to purchase health insurance, and the so-called Vitter Amendment that would bar the federal government from giving subsidies to Congressional members and staff to help them buy insurance in the Obamacare exchanges.

Here's the thing: It's not obvious that Boehner and Cantor can gather enough Republican votes to amend and pass a CR as they describe.

A CR along these lines would not achieve the top goal of conservatives: defunding Obamacare. And it would amount to a reduction in compensation for members of Congress (and their staffs) of several thousand dollars a year.

Assuming only two Democrats vote for this new plan (a reasonable assumption; that's how many voted for the last two House Republican versions of the CR), Boehner can only afford 17 defections. And Jennifer Bendery of the Huffington Post tweets that Rep. Peter King (R-N.Y.) says he already has 20 to 25 Republican no votes.

Rep. King also says he's got 20-25 GOPers ready to vote NO on the rule to bring up the CR with Obamacare delay in it. — jennifer bendery (@jbendery) September 30, 2013

House Republicans have been making clear this afternoon that they will not bring a "clean" continuing resolution up for a vote. But if these Obamacare-related amendments fail, where will that leave Republicans?

We've seen this play before: In December, Boehner advanced his "Plan B" proposal to limit the scope of the high-income tax increases that President Obama would get. But Democrats wouldn't vote for Plan B because it didn't raise taxes enough and many conservatives wouldn't back it because it raised taxes too much.

Ultimately, House Republicans couldn't gather the votes for a plausible tax plan and had to cave to Democratic demands for more taxes on the rich. If Boehner can't get the votes for his Plan C this time, that could be the prelude to a Republican cave on the CR.