The question is how did he rationalize it in his mind, or to other people? In terms of the latter, Liddy pitched the plan in the course of three meetings in the office of AG John Mitchell, who was also running Nixon’s campaign (so these crazy things weren’t just floated, they were floated inside the office of the Attorney General of the United States). At the first meeting, he pitched a plan involving the things you mentioned, including kidnapping and prostitutes, among other similarly outlandish ideas (called Operation Gemstone). Present at this meeting were five people: Gordon Liddy, Howard Hunt, John Mitchell, Jeb Magruder, and John Dean. Basically, from the accounts of those in the room, they heard the men out, but allegedly didn’t take it very seriously at all, and were pretty shocked, according to Dean. The coolest response came from Mitchell, who allegedly made a comment like, “This isn’t what we had in mind, Gordon.” When Liddy said the operation would cost a million dollars, he was was rejected outright. He came back a second time and asked for $500,000. He was again rejected on cost. The third time, he asked for $250,000 and was approved, though this version of the plan was severely whittled down, but still included a “bugging” operation, which lead to Watergate...

In his testimony before the Senate Watergate Committee, former AG John Mitchell famously said if he could go back in time, he wouldn’t just throw them (Liddy and Hunt) out of the office, but out of the window. The reason they didn’t is two fold, and I’ll give you the name of two people to answer this: HR Haldeman and Charles Colson. Haldeman was Nixon’s Chief of Staff, and undoubtedly the most powerful person in the Nixon White House not named Nixon. He demanded an up and running intelligence operation for the re-election, and put a lot of pressure on Jeb Magruder to get it done (this is because Democrats did it, and he wanted an even playing field). Colson was Nixon’s Special Counsel, and close personal friends of Howard Hunt, Liddy’s “partner in crime.” The combination of the two having an interest in the Liddy/Hunt operation; Haldeman for the dirt on the Democrats, Colson for his friend Hunt, lead to the plan eventually getting approved. Indeed, it was Colson’s personal call to Magruder to basically say the “Big Guy” wants this, that got it approved at $250,000.

For what it’s worth, Liddy, Hunt, Mitchell, Magruder, Dean, Haldeman, and Colson all spent time in a prison cell, because of their involvement in said activities.

Source: The Wars of Watergate, Stanley Kutler 1990