What would have happened if President Nixon had not chosen to resign?
If President Nixon had not chosen to resign in the face of the Watergate scandal, he almost surely would have been impeached and convicted. This would not have made much difference to him personally as his legacy was already in tatters. However, it might well have torn the country apart even further in political terms.
If he had not resigned, President Nixon would very likely have been impeached and very likely would have been convicted. The House Judiciary Committee had already voted to impeach him and the House as a whole was controlled by Democrats. An impeachment was almost certain. The Senate would have tried the case if Nixon had been impeached. The Democrats had a clear majority in the Senate and would likely have gotten a few Republican votes, thus reaching the 2/3 majority needed to convict.
However, this would have been a very painful process for the country. The impeachment process would likely have turned into a partisan battle. Republicans would have defended the President while Democrats opposed him. The country was torn as it was by the legacy of the Vietnam War and the other upheavals of the 1960s. An impeachment trial would have made things worse on that front.