Americans, incl. large majority of Democrats, think mandate unconstitutional.

[True Federalist (진정한 연방 주의자)]

the Dems' worse nightmare is to have Obamacare upheld by the SCOTUS.

The country's worst nightmare would be a partial overturning.  Must carry combined with the elimination of the personal mandate would destroy the individual insurance market, and yet would be so popular initially that it could not get repealed until said market was destroyed, with all the consequences thereof.

[True Federalist (진정한 연방 주의자)]

Weren't there several decisions that overturned parts of Plessy prior to Brown?

Depends on what you mean.  There were several cases prior to Brown that showed that particular examples of "separate" were not in fact "equal" and hence not constitutional under Plessy.  It wasn't until Brown that the court found that "separate but equal" was shown by practical experience to be inherently impossible to achieve and tossed out de jure segregation.