Do they need the presidency? They're stronger than ever right now while pointedly not having it, and aren't likely to get it next year. Sooner or later, they'll be able to break the Democratic hold on Congress, and that could change everything. In the long run, they need a Gingrich more than a Reagan, honestly, especially since they do better as insurgents.
You do need the Presidency in order to become legitimate and actually move forward with the big policy pushes. Winning the Senate or the House might cause a liberal or moderate President to make some deals, but the big push that changed the entire structure of American politics was Reagan's Presidency.
Since it was seen as 'successful', the Overton windows of American politics changed entirely. Without a Reagan Presidency, there's still a movement conservatism leader, but there's nobody articulating that message in the way Reagan did.
If Carter wins in '80, either because Iran butterflies better, the economy doesn't go quite in as deep a funk or the nation gets it's Volcker medicine sooner, then the entire message of 'if we run a real conservative, we'll win' is destroyed.
Actually, the better idea is somebody not named Jimmy Carter wins in 1976, who can actually work with the Democratic Congress. Let's just say Birch Bayh as a placeholder.
Somebody like Howard Baker or John Heinz or somebody like that is the nominee in '84. Yeah, they still might beat Mondale, but they'll still govern like a slightly more conservative version of Ford, or a slightly more liberal version of OTL's HW Bush.
Now, the knockdown effect's in 2015? Who knows. But, remember, the population didn't buy into the 'regulations are evil, tax cuts are magic, etc.' view of the movement conservatism just one day. They were pounded with that message relentlessly for years. If one of the main suppliers of that message isn't in the Oval Office, that makes Newt and friends job that much harder, because instead of Reagan doing the hard work of carrying the ball down the field, and Newt scoring the touchdown (the '94 wave), the ball is still down at the 30 or 40 yard line.
Yes, the New Deal coalition will crack. The South will crack. Both parties will become more parliamentary. But, there's plenty of seperate worlds where the modern GOP is far closer to even Bush's compassionate conservatism or hell, even a version of John Kasich's version of conservatism being the mainstream of the party, instead of it being the far-left wing of the party.