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The proposal -- which has also drawn support from Sen. Ted Cruz -- purports to ease passage of a more expansive Obamacare replacement bill by foregoing traditional Senate rules and seating Vice President Mike Pence as Senate chair for the vote.

Paul argued that with Pence as chair, he would be empowered to make decisions about what can be passed through budget reconciliation, a procedural distinction that has a simple majority-vote-threshold. That would allow Republicans to bypass the larger, 60-vote requirement that would otherwise be required to repeal and replace key components of the Affordable Care Act -- a major roadblock.

Paul -- who opposes the current GOP health care bill moving through the House -- said Wednesday on MSNBC's "Morning Joe" that leadership "is afraid of the Senate parliamentarian. But we've read the rules, and it looks to us like the vice president can sit in the chair, and the vice president can decide for the Senate what is reconcilable."

He explained, "the rules, the budget rules that everyone touts and are so arcane, they say the chair rules, and not the parliamentarian. The chair rules. The vice president has the prerogative of sitting in the chair, and if they want this done, the vice president should come to the Senate."

Paul's proposal comes as Republicans are under growing pressure to pass an Obamacare repeal bill -- but divisions within the party, a slim Senate majority, and legislative procedure have complicated those efforts.

Lacking large enough majorities in Congress to pass outright repeal, GOP leadership has sold Obamacare repeal and replacement as a three-phase plan, with partial repeal now and other key changes left for later.

The problem is that many of those key changes that are left for later will still require 60 votes in the Senate, which could take multiple election cycles to achieve -- something Paul's proposal purports to solve.

On MSNBC, he said that phase three of leadership's plan "is never going to happen," and argued that Republicans could instead achieve repeal and replace simultaneously with Pence, seated as Senate chair, declaring that a more expansive version of the bill is reconcilable.

Still, such a move would be a dramatic break from the way Senate rules have traditionally been observed, and could set an irrevocable precedent for legislating akin to "nuking" the filibuster for some Senate nominees. Paul seemed to acknowledge that his proposal faced long odds.

"Do you believe that is something that could happen?" asked "Morning Joe" host Willie Geist.

"Only if we have the guts to do it, and I don't know if we have the guts to do it," Paul replied.

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Rand Paul: Bring Pence to Senate to repeal Obamacare - CNN