Sen. Mike Lee, R-Utah, said on Wednesday that the Senate parliamentarian has told him that it may be possible for Republicans to push harder on repealing Obamacare's regulations than the current House bill, which contradicts the assertion by House leadership that the legislation goes after Obamacare as aggressively as possible under Senate rules.

"What I understood her to be saying is that there's no reason why an Obamacare repeal bill necessarily could not have provisions repealing the health insurance regulations," Lee said in an interview with the Washington Examiner, relating a conversation with parliamentarian Elizabeth MacDonough about reconciliation he had on Tuesday.

Lee also said that the parliamentarian told him it wasn't until very recently, after the unveiling of the House bill, that any Republican even asked her about the possibility of repealing regulations with a simple majority.

With a House vote currently expected on Thursday, Republican leadership is scrambling for votes, trying to stave off a backlash from conservatives that could sink the bill. One of the issues conservatives have raised is that the House bill leaves most of the regulations in place, thus not combatting one of the main complaints about Obamacare – its skyrocketing premiums and limited choice.

Because Republicans don't have 60 Senate seats to kill a filibuster, they have to pass a healthcare bill through a procedure known as reconciliation, which allows the majority party to pass legislation with a simple majority, assuming it meets a certain set of requirements, including that all provisions be primarily budgetary in nature.

Conservatives such as Lee have argued that Republicans should fight harder to argue that the regulations, which have a clear budgetary impact, can be passed through reconciliation. But House leadership and supporters of the bill have countered that the legislation already goes as far as possible. House Speaker Paul Ryan spokeswoman AshLee Strong, when asked about this by the Washington Examiner last week, said "We've worked closely with the Senate to carefully craft the bill to repeal and replace the law to the full extent allowed under the rules."

But having met with the parliamentarian, who plays a key role in advising the presiding officer of the Senate over what's in bounds during reconciliation, Lee is more convinced than ever that this is not true.

"One of the things we've been told over and over again is the bill was no more aggressive than it has been... in part because of Senate rules," Lee said. "And the Senate rules are something those defending the bill have repeatedly pointed to in defense of why they wrote it the way they wrote it. The parliamentarian said, there's not necessarily any reason that would categorically preclude you from doing more, both on the repeal front and the replacement front, all sorts of things are possible."

He continued, "What matters is how it's done, how it's written up. There are ways it's written up that perhaps make it not subject to passage through reconciliation, but there are other ways you could write it that might make it work."

To be clear, Lee wasn't suggesting the parliamentarian indicated that repealing the regulations would be definitely doable, but that, "There's no reason categorically to conclude you couldn't."

He added, "She was also saying until very recently, nobody had even asked her about it. And yet one of the arguments consistently used by those behind the bill is, 'This thing is the most aggressive we can pass and can get through Senate rules.' And it's just not true."

He also suggested that authors of the bill were inconsistently applying their understanding of the reconciliation process.

"That's one of the things that I find so stunning about this House bill," he said. "It still does include things that could be really problematic, and that some have suggested could even be fatal. So it's not as if they have crafted it in the most cautious manner possible relative to the reconciliation rules."

Asked to comment, a senior Senate leadership aide referred back to my own earlier reporting on the matter. Last week I cited sources within Senate leadership who said that Senate Republicans were engaged in ongoing discussions with the parlimentarian, the first goal of which was to get a bill to the Senate that doesn't automatically get ruled out of order on procedural grounds, thus blowing up the entire process before Republicans get a chance to offer amendments. Sources said leadership was open to pushing further, including on the regulatory front, though one aide described the possibility of getting rid of the regulations through reconciliation as a "long shot."