According to Wikipedia Deism is the belief that reason and observation of the natural world are sufficient to determine the existence of a Creator, accompanied with the rejection of revelation and authority as a source of religious knowledge. I suspect there are many people who could identify with the definition of deism and they more than likely already believe what it contains. I do not think these people will identify with the terminology however. I think they would be more likely to describe themselves as spiritual or for example a spiritual Christian, so as to hold onto their originally religion, but not necessarily the originally beliefs they were taught as a child.
I do not believe we will be seeing a church of Deism any time soon. Deism is usually used to describe how an individual approaches their own views, from within, and generally through outside observances. While there have been periods and history and there are sure to be periods in the future of this ideal taking hold, it doesn't mean it will displace major world religions at all.
No, Deism cannot become a mainstream religion after Christianity, Islam and Hinduism, because those religions are various Deist religions. A Deist religion believes that there is a God. All these religions believe that there is a god or God. But these three religions are so dominant, it is hard to imagine that any of these religions, let alone all of them, will die off in the world completely.
Deism was a more liberal choice back in the days of the founding fathers of the United States. But now it would be seen as archaic and old hat. We are not looking for a prime mover but rather for a spiritual or mystical experience that shows more of the deepest inner workings and mysteries of the universe.
Deism is growing in popularity, but the religion likely won't reach the levels of Christianity, Islam, or Hinduism. While it's growth is undeniable, deism is still farm from a mainstream religion, and practicers are outnumbered by followers of other religions in a big way. Therefore, it would take many more years for Deism to reach such levels.