There are currently 63 million registered democrats versus 47 million republicans. Combine that with the trend of hispanics and African Americans reproducing faster than whites and the lead in democratic voters is likely to increase.
Note that the Republicans continue to win their share of elections even though they are outnumbered. Neither party is going to disappear or even lose significant support. Democrats represent people who want to use government to help people and solve social problems and republicans represent those who focus on personal responsibility and traditional values.
Are either one of these world views likely to disappear? Not likely.