https://en.wikipedia.org/wiki/Clinton_health_care_plan_of_19...
https://en.wikipedia.org/wiki/Clinton_health_care_plan_of_19...
But that would clearly be erroneous.
For example, Hillary Clinton's effort in 1993 (your first link) was plowed under. And it came very close to happening with ACA as well. ACA passed only using the reconciliation mechanism in the Senate, and survived the Roberts court on a 5-4 vote. It's not inevitable at all.
The debate over universal health insurance at least 60 years old (Eisenhower's reinsurance proposal was intended to acheive that by providing public insurance to insurers against overly-high expenses), and the history of efforts in the domain provides no basis to conclude that something would have been adopted in the 2009-2012 term no matter who was elected in 2008.
It might have been "inevitable" eventually (though even that there is little evidence supporting), but whether it would have been now, or 20 years from now, or another 60 years before major steps were taken toward universal coverage, well, that's another question.