Ron Pollack, a longtime health care insider and executive director of Families USA, has floated a variation on this theme with the administration and congressional aides: a two-step process that would reassure House members their wishes would be met in the bill.

Under Pollack’s proposal, the House would take up the Senate bill only after the White House and congressional leaders struck a deal on key issues, such as taxes and the subsidies to purchase insurance. They would incorporate those changes into a separate budget reconciliation bill.

The House would pass both the Senate bill and the reconciliation bill, possibly on the same day. The Senate would then take up the reconciliation bill, which would require only 51 votes for passage…

This approach, however, would prevent any fixes that did not have a direct impact on the federal budget, such as changes to language on abortion and immigration and, possibly, even the insurance exchanges. The exchange question could be particularly problematic for House Democrats who have sacrificed the public option in return for the national insurance exchanges under the House bill.