I'd argue that Nixon wasn't in that boat, he actually supported formation of the EPA and such. Nixon's big contribution to the Republicans was his southern strategy (use of racism to win a previously Democrat south) and mis-application of domestic espionage.

"Government is not the solution to our problem; government is the problem."

President Ronald Reagan, in his first inaugural address.

Arguably a misquotation, probably misleading absent the context, and definitely an incomplete quotation.

Speaking narrowly and specifically about the economic crisis and stagflation of the late 70s:

In this present crisis, government is not the solution to our problem; government is the problem. From time to time we've been tempted to believe that society has become too complex to be managed by self-rule, that government by an elite group is superior to government for, by, and of the people.

The surrounding context doesn't really change/clarify that core message very much.

It does, it is saying the government had been the cause of the economic crisis of the time, not that it was generally the problem of all things.

the context makes it ironic even, considering they benefit from that exact sentiment to be elected.