Reagan wanted to be and turned out to be a transitional figure. Obama wants to do the same. They are similar in that regard, but they are different in a number of ways on policy. Ronald Reagan, though, would not be a fan of the current tea party's policies or positions, though.
Reagan supported a trickle down approach to the economy, he believed it would balance itself out and that there was no need for government intervention. He thought that if wealth was concentrated with the rich it would naturally 'trickle down' to the poor. Obama does not believe this at all. They take opposite approaches to the economy in very different times for the USA.
Obama and Reagan could not be more different. Reagan was pro-rich, Obama is pro-middle class. Reagan believed that the wealth of the upper percent would trickle down to the middle class; Obama knows it will not. Obama is a moderate, and Reagan was a moderate, in my opinion, so some might argue there is some similarity, but in ideology, I don't think they're close at all.
I don't think that Obama is following after former President Reagan's footsteps. He is following his own path and becoming a crusader on current hot issues like gun control and accessibility. Each President brings something different to the table and they are not overly comparable. Reagan began his career as a Democrat, but later switched to the Republican side.