For those who don't know what the HL-20 is, some links:
http://www.astronautix.com/h/hl-20.html
https://en.wikipedia.org/wiki/HL-20_Personnel_Launch_System
https://falsesteps.wordpress.com/2012/12/09/hl-20hl-42-the-personnel-launch-system/
It seems this small spaceplane from the 80s had a real chance of being developed, had the Russians not made the Soyuz capsule available to the American space program in the 90s. So let's assume that the ISS does not go ahead (maybe because the Soviet Union doesn't fall, maybe because the negotiations between the US and Russia for the ISS just fall apart) and the US commits to some sort of space program in the 90s (likely the rather threadbare "space station Fred", though maybe the Japanese and Europeans might still get involved in a joint station with NASA even without Russian involvement - though I doubt it, for various reasons). And the HL-20 becomes the basis for the eventual space station lifeboat.
What might this change?
My first thought, the HL-20 would either require man-rating the Titan IV (and engaging in ooky politics with the USAF) or for the NLS program to produce an actual rocket (and to man-rate that rocket). This could either mean that the Titan IV lives longer (and pays off more of its development costs, which is good for unit launch costs, but bad for the Florida environment) or the Titan IV is replaced earlier by something that looks an awful lot like a man-rated Delta IV (due to more commitment to the NLS) If the PoD is the SU not collapsing, the Cold War continuing may mean more commitment to seeing the NLS program through (though I doubt that the NLS would fulfill its promise to produce a VHLV, since the US just didn't need such a rocket in the late 80s).
Either way, while the HL-20 would get men up and down from the space station cheaper than the shuttle, it wouldn't do so much cheaper than the shuttle. The marginal cost for NASA to launch a shuttle in the 2000s was about $300-450 million and the marginal cost to launch another Delta IV in the same year was around $250 million or so. On top of the Delta IV marginal cost, you also have to add the costs of the HL-20 itself which could easily add up to another 50-100 million USD per flight. The Shuttle could get 7 men to the station and 14-25 tonnes worth of cargo (depending on the altitude and inclination of the station), the HL-20 could get 10 men up there with around 500 kgs of cargo. The prestige of shuttle launches, it's ability to carry more cargo and the desire to get the most value out of the shuttle system may mean that the HL-20 doesn't get launched often.
On the other hand, the HL-20 flying might mean that the shuttle is retired early - replaced either by the HL-20 itself, or by the HL-42, which might look more appealing once the HL-20 had proved itself. So maybe in TTL NASA would retire the shuttle in the late 90s, bringing welcome breathing room in the budget and also avoiding anything like the Colombia disaster.
And of course, the existence of either a man-rated Titan IV or a man-rated NLS would mean the US has the rockets to keep launching men into orbit after the shuttle had retired.
With the HL-20's main role being a lifeboat for the space station, we might see NASA pushing up the endurance of the HL-20 to hang about in the harsh space environment. That could put NASA in a much stronger position to send manned missions BEO.
Conclusions:
My instinct is that while NASA would develop useful hardware and systems during the 90s in this TL, the piddly space station Fred would hold it back from exploiting the full potential of a crew ferry like the HL-20. However, between the HL-20 (and maybe HL-42), better options for heavy lift vehicles for NASA and the shuttle retiring early (especially if that retirement comes before another serious accident), the 21st Century could be much more interesting for NASA.
What do other people think?
fasquardon