Under Cantor’s plan, the House would pass two different bills, a standard CR and a measure to defund Obamacare. Through parliamentary wizardry, though, the House would keep the Senate from voting on the CR bill until it had also voted on the Obamacare measure.

The meeting was part of what has been a difficult rollout for the Virginia Republican’s proposal, which is facing significant opposition from conservatives who would like to push harder to defund or delay Obamacare. The vote on the measures, planned for today or tomorrow, could easily go down in flames.

First, influential conservative outside groups such as the Club for Growth trashed the plan. Then, Senator Mike Lee, the original architect of the use-the-CR-to-defund-Obamacare strategy, ripped Cantor’s idea as a “face-saving” gimmick that added insult to the injury of abandoning the grassroots’ calls for a do-or-die fight on Obamacare. “It is not a plan to defund Obamacare — it’s a plan to facilitate the passage of a CR in a way that allows people to claim that they’re defunding Obamacare without actually doing so,” Lee told me.