I like to think that in those days, such nonsense as what passes for political discourse nowadays would be unthinkable, and that Limbaugh and Beck would be a bit more civil.
Anyway, they'd back Nixon all the way. They'd say that Woodward and Bernstein were providing aid and comfort to the enemies of the United States in a Cold (and Hot, in Vietnam) War. Woodward and Bernstein would, in their minds, be actively hampering the American effort to win the hearts and minds of the world, in the interest of personal gain. As the affair proceeded to the Senate, they'd get to denouncing the entire Democratic Party as power-hungry gits who'd sell the United States out for another term in office.
When Nixon gets around to resigning, he'd be lionized as the antithesis to the Democrats and the congressional officials probing his administration--where they sacrificed the strength of the Executive Branch on the alter of personal advancement, Nixon resigned from office and allowed a black mark upon his legacy in the interest of sparing the nation the struggle of an impeachment proceeding.