During the 1950's, the Republican party thought they had to become more Democrat like, due to reeling under FDR and then Harry Truman. Demo Lite in other words.
Given enough time and enough rope however, the Democrats self imploded in the 1960's. After the Great Society which was another boondoggle give away program, they stumbled into Vietnam and escalated that War. They lost the White house twice after that fiasco, and other then the doofus Jimmy Carter went on to win again and again, and again until 1992.
The Republicans don't need to become like the democrats. No one can predict the future. The Democrats under Obama may well get very careless (as if they aren't right now) and make the same blunders again. Ushering Republicans back to prominence.