America's Health Insurance Plans, the nation's largest industry lobbying group joined with the Blue Cross Blue Shield Association on Friday night to send a blistering letter to Senate Majority Leader Mitch McConnell, R-Ky., urging him to drop a compromise proposal from Sen. Ted Cruz that the groups say is "unworkable."

The proposal, which was crucial to winning over Cruz's vote, would allow insurers to offer plans that don't comply with most of Obamacare's regulations as long as they offer at least one plan that complies with all of them.

"As the U.S. Senate considers the Better Care Reconciliation Act, we are writing to urge you to strike the 'Consumer Freedom Option' from the bill," the groups wrote, referring to the Cruz amendment. "It is simply unworkable in any form and would undermine protections for those with pre-existing medical conditions, increase premiums and lead to widespread terminations of coverage for people currently enrolled in the individual market."

The statement by the influential insurance groups comes at a fragile time for the Senate bill. McConnell is hoping to hold a vote on the bill next week, but two senators have already come out opposed to the latest version, meaning the defection of any one of the remaining 50 Republicans senators would sink the bill or force a major rewrite.

If McConnell were to drop the Cruz provision under pressure from the insurance industry, conservative support for the legislation could collapse.

But Republicans may dismiss the letter, because, as noted by Cato's Michael Cannon, it is signed by the current leader of AHIP Marilyn Tavenner, who helped run the implementation of Obamacare when she served as President Obama's administrator of the Centers for Medicare and Medicaid Services.