I think it is telling that the two Biblical quotations that Byron from Slings And Arrows uses to elucidate his views in "Democrats and Deity," which analyses the Democratic Party's outreach to religion, both come from the New Testament:

First off, the Democrats are looking at faith from the wrong direction. They see the correlation between Republicans and their faith, but what they do not realize and refuse to admit is that the faithful choose to be Republican out of religious conviction. Those who attend church on a regular basis are constantly reminded that God tells us to "Be holy, as I am holy." Being holy means, among other things, defending the rights of the oppressed, such as unborn babies. It means honoring God above all things. It means putting God's priorities, and His understanding of right and wrong above our own. It means championing His causes when the society and culture around us oppose Him. It means agreeing with God and calling recognizing sin for what it is -- including the homosexual lifestyle.

For all intents and purposes, the "Republican God" is Jesus. Their house of worship is church. Abortion, homosexuality, and a laundry list of other actions are "sins." Obviously, a political party that does not support this does not recognize the important influence of American religion on our history and culture. Democrats, in attempting to adopt the same secular, inclusive approach one sees in other areas of party culture in order to invite people of faith - a term that applies to religious people regardless of their specific mode of worship, are playing politics with religion - while the Republicans' attempts to influence the votes of the churchgoing public reflects His will. A simple example of this inclusiveness is seen in their outreach efforts:
Yesterday, the Democratic National Committee sponsored its first convention caucus for "people of faith," and last week the party hired a Christian Church (Disciples of Christ) minister as a senior adviser on outreach to religious voters. On Monday night, the Democratic National Committee allowed a rabbi, William Hamilton of Congregation Kehillath Israel in Brookline, onto the convention floor to lead about 50 delegates in a postadjournment chanting of the Book of Lamentations to mark the Jewish holiday of Tisha B'Av.

Bryon claims:
The Republican party is comfortable with people whose values are informed by their faith, infact it embraces that. Faith-based values are antithetical to the Democrat party

Both parties care more about political values than religion. However, if your religion is close-minded and thinks unbelievers will die in a fiery orgy of destruction, you would probably fit better in the Republican Party than the Democratic. I think a person who believed the same American values of tolerance and compassion as the Founding Fathers would find the view of the Democratic Party not antithetical, but a perfect fit. As Jefferson noted in the section regarding religion in "Notes on the State of Virginia,"
But our rulers can have authority over such natural rights only as we have submitted to them. The rights of conscience we never submitted, we could not submit. We are answerable for them to our God. The legitimate powers of government extend to such acts only as are injurious to others. But it does me no injury for my neighbour to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg.

Would Jefferson deny basic American rights to homosexuals, as the Republican Party wants to? No. Would he call a homosexual irreligious, as Bryon does? No. This is what Ms. Garofalo was getting at (at about 4:50 in the interview [WMA] with Sean Hannity). Democrats are unimpressed by people who use their religion to come irrational or un-American conclusions. In some cases, Republicans are willing to accept this, as long as the proponents are Judeo-Christian.