What an encouraging comparison! That was the period when the Republicans did probably their greatest upsurge of organizing, building institutions like Young Americans for Freedom and other "New Right" groups that laid the groundwork for taking over the Republican Party completely and shifting national politics signficantly to the Right.
See http://www.theatlantic.com/issues/95dec/conbook/conbook.htm for more on the story of conservative success in organizing during the 1960s.
While I think there are big differences, the main point is that the mainstream has the tendency to completely dismiss a party that is short of a majority, ignoring how radically things can change with a shift of votes to kick them into the majority. The whole dismissal of the Democrats right now is equally misguided, especially given that recent elections have put them almost neck and neck with the GOP.
-- Nathan