The Senate GOP might do it but the Democrats would find single payer easier to ram through with 51 votes. That's why the GOP doesn't want to erode the filibuster for the Senate because they know the Democrats will rule Congress again one day and when they do the filibuster may the only fig leaf protecting the GOP.
If that's their hope then that's a false hope. Imagine a circumstance where the Democratic Party went through all the internal turmoil needed to make Medicare for All the official policy of their Presidential candidate, their Senate Leadership and their House leadership. Suppose in the meanwhile the Republicans continue to screw up healthcare reforms, as they are doing now. Supposing they then win the Presidency and majorities in both houses.
In that situation do some Republicans really think that the Democrats would turn around to their base and say "Yes we know we made Single Payer the centerpiece of the campaign, we know we won the election, but you are going to have to continue to worry about dealing with insurance companies, continue to pay massive premiums and co-pays, continue to worry about the possibility of a health crisis in your family leading to bankrupcy because muh Senate Traditions"
That's just fantasy. It that situation the filibuster would be gone in a heartbeat. If Republicans think that muh Senate Traditions are going to save them from Single Payer they're living in a dream world. The only thing that will save them from single payer is if they actually wake up and smell the coffee and bring in some effective healthcare reforms themselves. They will never get 60 Senate votes for this so one of the things they will have to do to avoid Single Payer is to kill the filibuster themselves.
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