Republicans would still have an uphill battle to retain the presidency in '76. The WH generally switches parties at eight-year intervals and the U.S. went through a nasty recession with surging inflation in the runup to '76.
Also, contrary to CW, I actually suspect Carter may still have been the Democratic nominee. While Watergate may have enhanced his appeal in the General Election, Carter winning the Democratic nod had much more to do with Democratic intraparty divisions and the primary calendar. Carter was the only candidate who actually ran in every primary and caucus and ran from the start - everyone else tried a pre-'68 strategy of declaring late, running in just a few states, and hoping for a breakthrough at the convention. He was also the only candidate capable of bridging the gap between Northern and Southern Democrats, and he also had much of the southern Civil Rights establishment - and hence a lot of the black vote - behind him.
Agnew still resigns, Nixon still nominates Ford (seeing as Connolly would be too difficult to confirm). Ford, though, probably doesn't run for president in '76. Reagan runs, as does George Bush, and perhaps Nelson Rockefeller or Charles Percy. Reagan wins the nod, selects George Bush as his running mate, and loses to Carter by 5-6 points. (Yes, OTL '76 Ford nearly won, but Reagan typically polled much worse than Ford in OTL '76 polls and his public image was not that different from Rick Perry today.)
Four years later, Republicans, lacking any major candidates, recruit former VP Ford to run against the unpopular Carter. Ford selects Jack Kemp as his running mate and defeats Carter in a landslide. Republicans take both the Senate AND the House (as no '74 Democratic landslide makes the margins far tighter).
From that point on there are various butterflies and changes resulting from different personalities in Congress and different personal styles...