Their claim is that the country has been ruined by the left, and they want to restore it to its former glory. It requires ignoring the fact that the country has taken a hard right shift since the time they are idealizing.
As for the cognitive dissonance, Stephen Colbert (during The Colbert Report) played around with this self-contradiction. His book is titled "America Again: Re-becoming The Greatness We Never Weren't"
Edit: autocorrect