The Union mentality of "I've-got-mine, Jack" when it came to healthcare was an issue too.
How would the US economy bear the burden of CHIP
Any Universal Program (and I don't consider the Public Option UHC; I think its just a safety blankets liberals use since they know they can't get a true national health now since they were hit so hard by the age of Reagan) generally cuts GDP spent on healthcare coverage (for example, I think the US currently pays 17 percent of its GDP to healthcare and that cost is rising, whereas universal system nations pay something like 10 percent or less.
I don't know how comprehensive the proposal was since I haven't investigated much into it, but if it is comprehensive so as to plug those holes that hemorrhage money in the current system, and with preventative treatment it would bring, it could well end up saving the US money. But given the sort of inconsistent Nixon economic policies that were tried to fix the economy in the 1970's, that thought could go out the window in the mess.
and would a Democratic or Republican President try to privatize it by introducing the OTL HMO system or something similar?
They might (probably a Conservative), but how it goes would depend on its popularity.