Hey David!
Talk about a holy grail, huh? Free home manufacturing starting with just light, carbon and a bottle of wee. Or a complex mix of salts and phosphates, take your pick. :P
From my understanding, thermoplastics behave somewhat like gels, in that above a certain temperature they melt into constitutent molecules, but at lower temperatures they either re-polymerise or just form an organised matrix that gives them their firm properties. Therefore if all that is required is the creation of a single molecule of a certain form, there is no reason you couldn't get an alga to do the job for you. Processing and extraction could then be standardised to select for large plasticky molecules, it's likely the same procedure would do roughly well enough for most plastics.
So given a raw broth that you extract a few grams of plastic from per batch, you could collect enough to melt into a spool that'll give you makerbot/reprap style feedstock. Personally I think it's high time they developed a pellet-fed printer, but it's non-trivial. With a pellet-fed printer you could just refine, shred and pour the plastic into the printer.
So, in principal, you could do just that: grow, refine and print with your own plastics. I don't doubt it'll happen someday but it's impossible to predict when! A near-term homebrew thermoplastic would be possible now if there were one that you could use as-it-comes, but my understanding is that most "bioplastics" are actually chemically refined somewhat from natural precursors. Perhaps a natural wax could stand in for a bioplastic if you're willing to accept a lower melting point and a possibly brittler quality. But a collection of appropriate conducting, semiconducting and structural plastics that we can "brew" directly and extract at home will probably take a while.
I'd predict it as a mid-term landmark in synthetic biology, somewhere between the beginnings of genome engineering and the endpoint of "print me a horse".