California voted to the left of the nation when Democrats lost for years:
1972: 55-41 Nixon vs 60-38 Nixon nationwide
1984: 57-41 Reagan vs 59-40 Reagan nationwide
1988: 51-47 Bush vs 53-45 Bush nationwide
However, California ran to the right of the nation when Democrats won:
1960: 50-49 Nixon vs. 49-49 Kennedy nationwide
1964: 59-41 Johnson vs 61-39 Johnson nationwide
1976: 49-47 Ford vs 50-48 Carter nationwide
The only time California ran to the right of the nation in my lifetime was in 1968:
1968: 47-44 Nixon vs. 43-42 Nixon nationwide
One reason for these results is that from 1960 to 2008, California was THE battleground state. There were many books that spoke of this. As a kid interested in politics, I remember reading a book around 1971 from my public library that predicted that the Democrats would beat Nixon; it predicted that the Southern states would return to the Democratic fold, and that "California would be THE battleground for 1972"; it would be where the election would be decided.
Was any election "decided" by California? One could argue that the 1968 Presidential election was. Nixon carried California by a mere 3 points, and HHH was surging on Election Day. A shift of 1.5% of the votes in California to HHH would have thrown the election into the Electoral College, where it would have become interesting. That didn't happen, but what if it had? I would state, however, that this was the ONLY time that California was, truly, a "tipping point" state of any kind.
Not true it voted significantly to the right of the nation in 1980
Yes, that was an exception, but there are several big qualifiers here:
1. Reagan only ran 2% ahead in CA than he did nationwide.
2. Reagan was identified with CA in a way that Nixon wasn't. Nixon was a national figure from 1952, onward.
3. In Congressional races, the Democrats did rather well. Democrat Alan Cranston was re-elected to the Senate. In the House, only three (3) CA Democratic incumbents lost. All three were old and had been hanging on for some time.