Would Reagan be Considered a Democrat, Now?

I have found this video comparing speeches between President Ronald Reagan and President Barack Obama about closing tax loopholes to millionaires.  The cuts of the video show eerie similarities between the both men's speeches. It raises the question has the Republican party gone so far right that Ronald Reagan would be considered a Democrat in this political climate.  We know now that President Nixon would be with the Republican war on the EPA, but Reagan would be disastrous blow to Republican ideals. Propping up a man who would agree with your opponents more than his party. It is troubling. Here is the video