There were calls after AS11 to completely shutdown the program from members of Congress. Also even with AS17 flown, we left alot of hardware (2x complete ASV & 2x ASIas , plus 1x CSM, and 2xSIVs). Alot the money was actaully flying them.
I'm not sure what an ASV or an ASI is supposed to be. That aside, note that OTL Apollos 15, 19, and 20
were canceled. Apollo 20 was canceled to free up a Saturn V for Skylab; Apollos 15 and 19 were canceled for budget savings (which were quite nominal, since all of the expensive procurement had already been done). Apollos 16, 17, and 18 then flew as 15, 16, and 17. So I agree that there certainly was some opposition to further lunar missions. However, it's worth noting here that there's a somewhat famous memo written about this time from Caspar Weinberger (head of the OMB at that time) to Nixon which essentially advocates
not canceling missions past those OTL canceled, and which Nixon responded to by writing "I agree with Cap". Given that Congressional opposition to further lunar missions was relatively diffuse and weak, and Executive support was relatively concentrated and strong, it seems unlikely that further cuts would happen. The success or failure of Apollo 13 really has little to do with it, if anything IOTL made moon missions look riskier and more likely to fail. Sure, NASA pulled a rabbit out of their hat...
this time. What about
next time?
In my opinion, the pressure from the scientific lobby would have been enough to ensure that at least
one J-class mission with Harrison Schmitt on board would have flown by the end of the Apollo program (they already managed to get Apollo 15 canceled instead of one of the J-class missions, and moreover got Joe Engle kicked off Apollo 17; not to mention forcing the intake of the Scientific Seven and Excess Eleven), and that means continuing to at least Apollo 15 (all earlier missions were H or G class, which were much less scientifically capable). The savings from canceling two more Apollo missions would have been quite small, as noted above, since the hardware procurement had been completed and paid for already, and would have caused a roughly two year gap between the end of Apollo and the beginning of Skylab flights, so there is then a reasonable basis for continuing those missions in that time (recall that in 1973, when they chose not to continue Apollo past ASTP, that Shuttle was being projected to fly as early as 1977, so the existence of the later long gap is not evidence that the earlier short gap would have been ignored).
Trivia note, by 73-74 Congress oppositon was strong enough to actually put a line in the budgets forbidding NASA to mothball the remaining hardware for future use.
That's certainly not true, since Apollo hardware was maintained in storage (ie., in mothball) until mid-1976. What is true is that in 1973 all hope of flying Skylab B ended because of the projected cost of doing so, the successful launch and rescue of Skylab A, and the beginning of serious Shuttle design work. This had very little to do with Congressional opposition to spaceflight, except insofar as that had led to the demise of the more expansive post-Apollo program plans (which would have kept Apollo production lines open) and budget limitations that prevented using Skylab/Apollo and Shuttle hardware at the same time. Skylab was also somewhat technically incompatible with the Shuttle system (in particular, it used a 5 psi 80% oxygen/20% nitrogen mix instead of the sea-level atmosphere aboard Shuttle), so there were perfectly good reasons not to launch a space station with a limited lifetime and utility at any rate, budgets or no.
So don't under estimate both the opposition to the space program, and the lack of interest amongest the majority of the public post landing.
But what effect did Apollo 13
have on that? That's the question that's being asked, and to me it looks like the answer is: Very little. Sure, Nixon and Mondale and Proxmire and the rest will pare down NASA's ambitions, they're going to want to cancel some Apollo missions. But what basis is there for asserting that a successful Apollo 13 will either avert or accelerate those moves?