No Watergate means that Nixon has the political capital to try and take on the Democrats over the health care issue. IIRC, what he wanted was something similar to the public option plan being discussed today, but the AFL-CIO and Ted Kennedy shot him down because they were hoping for a better deal under a Democratic administration.
With Nixon's approval still relatively high and 1976 looking like a loss, I'm inclined to think that Kennedy and the AFL-CIO might accept the measure in the short term. Let's say a public option is passed, much to the chagrin of the Republicans, and Nixon gets even more popular. The 1976 Presidential Election is probably going to be fought on the legacy of Nixon, but on a more positive note than OTL.
With the Republicans, Nixon favored Connally as his successor, but that doesn't mean others aren't going to jump into the race. Vice President Ford probably enters, as well as Governor Ronald Reagan, and maybe a liberal Republican like Pete McCloskey or Nelson Rockefeller. With help from Nixon, I think Connally pulls off a victory running as a bit more conservative version of the otherwise progressive incumbent. Connally probably picks a more liberal running mate, however, like McCloskey or Rockefeller.
The Democrats aren't going to nominate Carter, IMO, simply because he won't have the same appeal to the nation that OTL's Carter did running on his clean image. Kennedy is smart enough to see that with Nixon's popularity, '76 isn't going to be winnable, so I think he'd sit this one out, as well. That leaves Henry Jackson, Jerry Brown, etc. The Democrats probably try and overcompensate for their 'mistaken' choice of McGovern in 1972 and nominate Jackson. Jackson probably goes for Carter as his VP choice.
Jackson and Connally is probably going to be a close race, but in the end, Connally should pull through because of Nixon's popularity. His cabinet is going to look a lot like Nixon's, but his presidency is going to be a lot like a mix of the Ford/Carter years. He begins to deregulate industry, but is unable to deal with the staggering inflation, etc. In 1979, Ronald Reagan announces his intent to challenge Connally from the right.
On the Democratic side, Kennedy hedges his bets and enters the race, as does Carter, John Glenn, and some others. Kennedy, however, will be the favorite in any match-up, primary, general election, or otherwise.