Thinking about it Nixon not going could hurt him and the GOP far worse than his actual resignation.You see when it comes down to it Nixon's choice to resign while not exactly a "mea Culpa" did at least draw a line under most of the affair (Fords pardon obviously not helping matters but that's a seperate issue) and dumped the blame squarely where it belonged.
In doing so Nixon can be seen as being punished (even if he never faces trial) the matter is over and done with and the country can move on. If he doesn't do this, then we have two and a half years more of a man most people already believe is a crook in the white house.
And losing the tapes would only make things worse, remember in OTL there is a seriously fishy 18 and a half minute gap on the tapes (as well as a couple of conversations that rather convinently "weren't recorded") so with all the tapes missing it will just add to the questions of just what the hell was on those tapes.
If Nixon somehow survives this then the GOP is wiped out at the '74 elections and probably even worse than happened in reality, you then get two years of President and Congress at daggers drawn even assuming there isn't a second attempt at Impeachment, and instead of having six years and a useless democratic president to distance itself from Nixon, the GOP has barely three and a half, and people will solely remember watergate, not all the stuff Nixon did earlier in his Presidency, or for that matter all the work the GOP did after '74 to distance itself from the scandal.
What I'm trying to say is that if the resignation and Pardon don't draw a line under the scandal then you get two more years of digging, and even if the press and congress don't find the smoking gun the infighting makes an even bigger mess than the real thing ever did, and for the next decade or more the democrats can point at the Republican's and say "You think we're bad these guys gave us Nixon," and the Republican's are likely to have been seen as proping up scum for two years (especialy if their votes blocked impeachment) and can't just put all the blame on Nixon and a few other bad eggs.
At best it hurts their election chances for a long time to come, at worst it could tear the party apart and even Reagen has an uphill battle in 1980 (after Carter he'll probably win but it will be a hell of a lot closer).
(Sorry for the long winded reply everyone)