If I may, here is my thoughts or nickles worth:
Look at vs 19 of Romans 1 which in context is connected to vs 18:
For what can be known about God is plain to them, because God has made it manifest to them
This portion is directly related to vs 18 which states the "wrath of God is revealed", here man knows of God's wrath or judgment.. "against all unrighteousness" ... here man knows of sin (unrighteousness) and by contrast must also know it's polar opposite - Righteousness. And His judgment revealed is against "those who hold the truth in unrighteousness" .. knowing but rejecting. But what is most interesting is that these things are made known to them BY GOD.
Not only there but as you read the rest of Romans 1 you can see 3 interesting things that man comes to know specifically.
1) Sin;
2) righteousness;
3) Judgment to come
What makes this so interesting is that Jesus stated the Holy Spirit into the 'world' to convict the world of:
1) Sin;
2) righteousness;
3) Judgment to come.
From here it appears that man's intellect and rational ability are not enough for him to understand these things by himself. God must reveal them to man.
Another point just as important is that mans heart once he chooses not to believe becomes darkened/hardened (vs 21), and continuing in this manner and going from bad to worse (vss 22-23), we see it was AT THIS POINT (wherefore or because of this) God gave them over... it was after their rejection of His truth(s) he turned them over to have what they wanted most (separation) from Him.
This is important because it reveals something spectacular about God's interaction with unregenerate man.. that He not only DOES but IS doing so. It is important also because we see they weren't set aside and just left alone by God, and that God only works upon those whom will believe.
Personally I believe this argument can and SHOULD be made by Calvinists in that God does indeed work upon the unregenerate to the point they indeed do know not only of but somewhat about Him. However it is not done in such a way that compels them to come, but to only acknowledge Him and their own lostness. In this, like the very passage in Rom 1 (and even 2 shows) they are without excuse because they knew the truth, but rejected it. I believe this is seen enough in scripture give extremely strong support for this idea (though it is not my belief), yet it is not something you very often at all, though I have run across here and there of late. Regarding this kind of view I could at least agree with them more as I don't see scripture declaring that God does not work upon those who will not believe. (as evidenced here, He does, to some degree)