With the current makeup of Congress, that won't happen for a long time...if ever. Senate would need 60 votes and they look to fall BELOW 50 in the next election cycle.
Of course, administrative applied defacto single payer comes about as the insurance industry and hospitals fail. The broad administrative administration is built into the law. They may need a bill or two at the very end of private insurance and hospitals, but they can have those markets killed dead by the time it is required.
I really don’t think you understand the ramifications of eliminating the mandate but leaving the rest intact. Suddenly the insurance companies will be forced to insure anyone with no pre-existing conditions limitations. This will lead to chaos and skyrocketing rates in the health insurance market, and as soon as consumers figure out that they can just forgo the health insurance until they get sick, the health insurance industry will go kaput. No more health insurance for anyone.