"Will his beliefs have an effect"
Sure - just like any other president, he "beliefs" will effect his thoughts. However, since he WROTE "Obamacare" to begin with for Massachusetts, that's probably a predictable path, and in the final analysis it's CONGRESS that will have the major effect on what actually gets done - if anything.
My GUT feel is that Obama will be re-elected.
And remembering God's words - Prov 16:
33 The lot is cast into the lap; but the whole disposing thereof is of the LORD.
We'll get the leadership that HE desires for us - hopefully NOT the leadership we deserve. But if we want to think we actually have some control over it with our "Elections" - then so be it.