Without vietnam to make it look like a winnable election, Nixon stays out. LBJ handily beats reagan-rockefeller that year with HHH winning against a second attempt at Reagan in 1972. HHH's terms are a bit rockier what with an energy crisis to contend with but he's remembered as a good president thanks to legacies such as national healthcare, a basic income, guaranteed income/workfare and generally making the US be closer if not yet at full on social democratic levels.
HHH's successor Muskie loses to a tanned, fit and rested Nixon in 1980. Nixon's goatee is often cited as what helped propel him to the top. You get a Gaullist/tory type GOP with Nixon and whatever literally who tier in OTL GOP representative/senator succeeds him in 1989. Probably another moderate if obviously left-leaning dem and not OTL's rockefeller republican in democrat clothes clintonites in 1996. Odds are the GOP wins again in 2000 thanks to a stronger coalition -- no religious right, more of a working class vote, bigger nonwhite presence in GOP due to differences in coalition
My guess is various things like timing of recessions means you'd likely see democrats in office 2009-2017 and the republicans winning in 2016. Maybe a poorly timed recession means they lose in 2020 idk. Regardless they'd either be different spins/versions of OTL figures or people who are deeply obscure in OTL.
Democrats: More economically left, more "populist", less "respectable" white collar/yuppie, split on guns. More union presence an less Activists thanks to nothing like the Mcgovern commision reforms.
Republicans: More socially big tent, significantly to the economic "left" of our GOP, less blatantly RELIGIOUS even if still overall conservatives, gained a right-populist wing after the 70s and 80s thanks to former wallacites[1], less southern foxused.
Less polarized, more swing states than OTL.
[1] No attempted assasination or ending up in the wheelchair means the AIP sticks around longer as a party.