Frodo, do you know what a filibuster is. Democrats have pledged to use a filibuster on any social security bill that: raises the retirement age or introduces any privitisation. That leaves only raising the payroll tax limit as a viable alternative. 55 is not a governing majority when the other 45 don't back the bill.
And Republicans have the power to override any filibuster Democrats might launch by using the 'nuclear option'. That they haven't done.
Internal divisions are a far more serious threat to any effort Republicans might make to privatize Social Security than anything Democrats might do.
Then I'll assume we can count on your support if the nuclear ption ever comes back up for a vote, as you've declared yourself a majoritarian?