The new Democratic majority in the House is unlikely to make any serious attempt to impeach Trump, but they are certainly going to subject him to a very high level of scrutiny. That will include a demand for his tax returns. He has made it clear that he has no intention of giving in on that issue. Litigation will ensue.
Trump is going to put a lot of faith in the willingness of what he will see as his new Supreme Court majority to protect him from the House. The Chief Justice, on the other hand, is going to remember how Chief Justice Burger managed to get a unanimous vote out of the Court on the Watergate tapes issue. He is very sensitive to the public perception of the Court as a purely partisan body, and the last thing he needs is a series of 5-4 votes protecting Trump from a variety of public records demands.
Will he succeed? That will be one of the key questions over the next two years. On this point, I make no predictions.