I'm not sure what you mean by "At what point or series of years did we become so politically focused on one type of religion?" Are you asking when Christianity first became significant in American politics? If so the answer would be that it was significant essentially from the beginning - as early as 1800, Federalist political propaganda was calling Jefferson an atheist, and lambasting Republican links to the militantly anti-Christian French Revolution.

Regarding Lincoln's personal religious views, he was fairly quiet on them himself. He never joined a church, and when running for Congress in 1846, his opponent accused him of atheism (which he denied). On the other hand, during his term in office, he not-infrequently used Christian rhetoric such as in his Second Inaugural Address. After his death, several pastors claimed that Lincoln had "[given] his heart to the Lord Jesus Christ" during his Presidency. He definitely did have repeated emotional crises while in office, but there aren't any documents to back up the pastors' statements.