The Soviet Union "wins" the Cold War as Americans everywhere are supremely sad and pissed off at the deaths of millions of people. They demand a complete end to the nuclear arms race and peace with the Soviet Union. Kennedy resigns as there is a huge backlash to his hawkish policies; Johnson takes over and tries to do damage control.
He ends secret spy plane programs and restarts arm talks with Khrushchev, who agrees to limited nuclear disarmament. Khrushchev also sends Soviet humanitarian aid to New York City and the surrounding area, as part of a political ploy to show the Soviet Union was benevolent and peaceful compared to the reckless United States. Johnson also directs the CIA to pull out of other countries and stop trying to kill Castro.
The 1962 midterms are devastating for Democrats, who lose control of the House and Senate due to backlash over the tragedy, Republican isolationist ideas, and a depression caused by the destruction of the financial base of New York City. Johnson is able to get the economy booming in 1964 by cutting defense spending and redirecting it to economic stimulus programs(congressional Republicans remain largely moderate) and ekes out a close reelection.
He spends his second term battling the counterculture and Southern Democrat anger over his civil rights plans, which still get passed in 1963/1964. So basically like OTL, but there is no Vietnam War. South Vietnam falls 5-10 years earlier than OTL due to no American military support and Ngo Dinh Diem remaining in power.
It's unclear who wins in 1968, but most likely a Republican will win due to the party turning back to isolationism and aligning with the will of most Americans TTL.