There is a movement which has been gaining momentum in the last few decades, although i couldn't say whether or not it were gaining adherents--which is secular humanism. I suspect that Romney is referring to that. It is possible, although i do not claim to know it, that among members of the religious right, secular humanism is now referred to in a kind of short-hand as secularism.
In the very early days of this site, i had a long argument with O'George about secular humanism, and my position was also that secularism cannot be a religion, and basically accused O'George of indulging the Chicken Little syndrome. However, subsequent research has shown me that, at least insofar as concerns secular humanism, O'George is correct to describe it as a movement. Furthermore, it reminded me of a group of militant atheists of whom i became aware when i was living in Columbus, Ohio, whose atheism was, functionally, a religion for them (with "science" as their "scripture," and about which they understood as little as one can expect your garden variety fundamentalist to understand about the historical and literary antecedents of biblical scripture). I was completely put off by their militancy and their attitude toward not simply religionists but toward anyone who dissented from them. I rather quickly declined to participate in their activities, even though i had first encountered them via a woman whom i found attractive--they were sufficiently "off-putting" that i drifted away from her.
You can read the Wikipedia article on secular humanism here.
You can visit the home page of the Council for Secular Humanism here.
Whether or not Mr. Romney was referring to secular humanism, the existence of organized secular humanist groups would certainly lead members of the religious right to believe that they are involved in a battle with "secularist" forces. Romney, or his handlers, may be attempting to exploit such a sentiment.