just get rid of the vietnam war: LBJ is most successful president after FDR, the new deal coalition breaks up slower and LBJ wins in 1968. Someone passes nationalized health insurance in the 1970s or something and when the new deal coalition breaks apart the US is much further to the left and has more core programs embedded within the fabrics of American society. Reagan or someone like him still comes along but just as he failed at touching social security/medicare/medicaid he couldn't touch whatever program the left passes in the 60s-70s.
So basically the US looks more like the UK than it does US otl