Yes, and not always.

Support for Nixon was extremely strong among conservative circles, particularly in the South, despite the scandal. Opinion polls taken in late 1973 and published in the first week of 1974 showed vast support for the charges against Nixon, but on actual impeachment, the country was much more divided.

In the South, there was a popular belief that the moves against Nixon were "little more than a Northern liberal plot," possibly even a Communist-inspired plot, to embarass the president. When Nixon visited Jackson, Mississippi in April 1974, he was greeted by a cheering crowd of 10,000 people. The local paper, the Jackson Daily News, published a front-page editorial saying Nixon had been "electronically lynched each evening in the living rooms of the land" and that the media was to blame for the president's troubles.

Nationally, William F. Buckley Jr., editor of the National Review, wrote a lengthy and impassioned defense of Nixon in the May 20, 1973 issue of the New York Times. Buckley wrote that it was inappropriate to judge the president by normal standards, and in fact what he did was not out of line with the actions of previous presidents. "The evolution of the Presidency slowly, but not less certainly, transformed the office and presented the republic with an unwritten qualification," Buckley wrote. "It is this: You must not impeach and remove a President merely for the purpose of punishing him."

There was, of course, ample response to Buckley.

You might consider that Nixon had a large base of support (after all, he was elected President twice, and if you consider 1960, was nearly elected three times) that gradually eroded as more information became published. The New York Herald Tribune had a fairly typical pro-Nixon editorial stance before it went out of business in 1966 (h/t /u/texum for the clarification), as did the Manchester Union Leader. As the scandals of Nixon's second term gained light (credit the Washington Post here for picking up on stories that others discounted or underplayed), Nixon's support began to erode. The conservative magazine Ideas (it folded in 1975) was one of the longer-lasting defenders, as was William Safire, Nixon's speechwriter (before an abrupt resignation), penned a book partially in defense of Nixon. "I'm writing this book sympathetic, but not sycophantic," Safire said in 1973, two years before the book was published in 1975.

When Nixon's transcripts became public in 1974, even people like Buckley deserted him. Only the hardest of hardcore supporters stayed with Nixon, and with friends in the House and Senate saying that impeachment and conviction were likely, Nixon resigned.

Also: did editorial boards publish retractions or apologies after-the-fact? Most interestingly: was anyone tracking this on a meta-level like we might expect with the internet today? Did anyone publish "scorecards" of how corruption in the Nixon administration was reported by various publications?

In his book "Watergate: The Presidential Scandal that Shook America," Keith Olson describes how the different newspapers around the country turned against Nixon as the scandal unfolded. He cites conservative and liberal editorials from papers in large and small cities to give a general idea of how opinion changed. I believe that he stressed that, after the "smoking gun" tape was released that showed Nixon was guilty of obstruction of justice, even the most conservative papers called for impeachment. There was disagreement over whether Nixon should resign or let the Congress remove him from office, with the more conservative papers favoring the latter. I don't have the book on hand at the moment, but I really recommend it for a more in-depth answer on the press' reaction to Watergate or the scandal in general.

Follow up question: what usually becomes of the presidents cabinet members after a midterm change of president? E.g. After Nixon's resignation or Kennedy's assasination.

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Follow up questions:

Does anyone have newspapers/microfilm from any news sources covering the scandal?

Was there any speculative gossip in the news, or did they simply not cover it until facts were officially released?

What would the public have known at the time? For instance, when the lawyer team including Hillary was combing through records, was the public aware of the extent of the investigation?

How long did the scandal last, from speculative gossip, if there was any, to resignation?

Was the public aware, or was there speculation, gossip, hearsay, etc, during the election; or did it all begin to surface afterward? Did the public actively elect someone whom they suspected to be a criminal?

Were there Republican leaning and Democratic leaning popular news outlets at the time? How did their coverage differ?