We all know there ain't no lower limit to the worst case, but I doubt this TL was written to showcase the utter impossibility of a McGovern victory since Nixon would be sure to push the Ragnarok button before he could take office. The next fallback from a legacy of civilization ending Armageddon would be to figure out how a Kissinger-Nixon team-up could RF the new administration with dilemmas impossible to resolve without dishonor of some kind; bonus points if it is so cleverly arranged that reasonable people see the timebombs and landmines going off as McGovern's fault.
I am not clever enough for that sort of N-dimensional chess and think that while Nixon and Kissinger might think they are that clever they are mistaken; a predictable outcome is McGovern has to deal with the known landmines he took on in running and a handful of extra headaches that do not make the outgoing administration or defeated party look particularly good, or perhaps some moves that do make them good but that's because they are good, good assets for McGovern to enter office with. The latter segues into the radical notion that Nixon actually cared to be a good US President in service of recognizably rational US interests. And/Or that Kissinger, who started out in the Johnson Administration after all, has some hopes to either be taken on board by McGovern or failing that, to be on the short list for Secretary of State when the next Republican takes office, and therefore would be trying to put out any fires Nixon might wish to start or accidentally start in his current state of mind.
It is the nature of politics of course that one man's solution is another's idea of a problem. At this point OTL, the ideological rift between the two dominant parties was still rather small, with lots of liberal Republicans (whose liberalism was still distinct from that of a liberal Democrat to be sure) and very conservative Democrats; the difference between the parties was more one of the mass distribution on the spectrum as it were--with moderate to liberal Democrats being notably but not dramatically to the left of the center of mass of moderate to liberal Republicans, the latter being strongly concentrated in the center with a fairly substantial right wing balancing a fairly liberal left wing, while the Democrats were more bimodal, a distinctly to the left (but never too radical, that might change a bit as post-Vietnam politicians of the Tom Hayden type start picking up seats) wing bunched around some point somewhat to the left of the Republican moderate-liberal divide, and a Dixiecrat/quasiDixiecrat (people like Yorty of Los Angeles, not Southern but of Southern mentality) wing--and in turn these conservative Democrats are New Deal heirs who have no problem with tax and spend Big Government in the form of pork for their districts--Wallace types essentially.
So, separately with their respective wings mashed together, both parties are pretty similar in terms of mode, median and range, though the Democrats have fewer absolute centrists I suppose. Thus, while a given foreign policy will be welcome to some in Congress (speaking of House and Senate collectively here) and heresy to others, both parties will have both friends and foes in their ranks, and it is probably true that there is no particular policy any President can have on any important issue where both parties won't produce enemies of it, quite possibly two sets attacking from both left and right. But the differences in policy a President from one party would have from one from the other would be rather subtle, and either President would have pretty much the same enemies, filtered with more or less weight to one side or the other. At this early date, it would be hard for a President to leave an ideologically opposed incoming rival a time bomb that is also a boon for the next one from their party's election.
The centrist consensus on foreign policy, the cover for the claim "partisan politics stops at the ocean shore," is probably still going to be dominant and nothing Nixon seems likely to be able to do seems liable to both pass muster within that consensus and be able to shove McGovern out it. Short of WWIII of course!