Assuming everything plays out as it did the OTL, Nixon, if he were stupid enough, could hold out until he's actually impeached sometime in late August/early September of '74.
Once the "Smoking Gun" tape comes out, Nixon is gone. In the OTL, he lasted less than 72 hours after the tape was released. The tape was such a slam dunk that ten of the 11 committee members who had earlier voted in July against the three articles of impeachment announced they'd vote for the same articles when the vote came to the House floor. Also, as Solomaxwell correctly points out, there were already enough votes in the Senate to convict Nixon.
(IMHO, Nixon held out too long in the OTL. Once Felt leaked both the existence of the taping system and the possible contents of the "Smoking Gun" tape to the Post, contents which Dean and others confirmed, Nixon was done even if he destroyed the tapes.)
There are many PODs which could minimize Watergate and keep Nixon in office at varying levels of "lame duck" status. Keeping Felt somehow onside is one, hiring someone other than the Cuban version of the Three Stooges to commit the break-in is another.
As previously sugested, immediately throwing CREEP under the bus, along with a few select staffers who could be relied on to keep their mouths shut even when convicted, could be another possibility. Having a president who has been running on a law & order platform since 1968 acting as if he's imposing a little law & order within his own administration might actually play well with the voters.