Sen. Mike Lee is suggesting that a ban on federal funding for abortion in the House health care bill might not survive a procedural challenge on the Senate floor.

In an opinion piece for The Heritage Foundation’s Daily Signal, the Utah Republican wrote that under Senate rules, the House health care bill might not be compliant as a reconciliation bill (a budget measure that only requires a majority vote). He said provisions will need to be stripped to comply with the so-called Byrd Rule.

Under the budget rule named for the legendary West Virginia Democrat Robert C. Byrd, reconciliation bills bypassing the customary 60-vote requirement to limit debate in the Senate must be about the federal budget, and avoid policy language that is “merely incidental.”

“This is a bad bill — one that will almost certainly be made worse once the Senate parliamentarian gives it the ‘Byrd bath’ required for it to go through the Senate with just 51 votes,” Lee wrote.

The two-term senator said the process of scrubbing the bill through the Senate parliamentarian’s office — known as the Byrd bath — “in this case could be used to knock out key provisions of the House bill, including prohibitions on taxpayer funding of abortion and price controls on insurance premiums.”

Lee has been among the Senate conservatives most critical of the House bill, which House leadership has been insisting is the only measure that can get through both chambers. Leaders say they have worked to comply with the Senate’s parliamentary peculiarities.

Elsewhere at Heritage, Mike Needham, the CEO of Heritage Action for America, suggested conservatives look no further than the White House to stand strong against GOP leader’s bill.

On a Monday call with reporters, Needham touted current Vice President Mike Pence’s 2003 vote, as a congressman, against the Medicare Part D plan as a model for conservatives under pressure from House leadership now to support the GOP health care bill.

“If you were going to write a book on how Mike Pence got to the vice presidency, there would definitely be a chapter on that courageous stand that he took,” Needham said.

A move to strike the blockade on funding for abortion services if such language is “Byrd-able” would seem sure to cost votes in the House among social conservatives.

Like Kentucky Sen. Rand Paul, Lee proposed calling up and sending to President Donald Trump a new version of the 2015 repeal and replace measure that has already been determined to meet parliamentary scrutiny.

“Let’s pass the 2015 repeal bill that Republicans in both houses of Congress voted for just 15 months ago,” Lee wrote Monday. “Once Obamacare has been properly sent to the dustbin of history, then we can begin a deliberative, open, and honest process to reform our nation’s health care system.”

Kerry Young contributed to this report.