In the movie Lincon, who are the more conservative Republicans? What do they want in order to pass the 13th amendment?

They want to ban the slavery. If Congress didn't act on slavery right away, it was going to do so eventually. Of course, it's always possible that Lincoln feared any delays might jeopardize the coalition represented in the film by the differences between Thaddeus Stevens and Tommy Lee Jones characters. The movie deals a lot with Lincoln's fears regarding the Supreme Court and what they might do to his Emancipation Proclamation. What is left unmentioned was the fact that the Unionists were ruling the Supreme Court after 1863. Anti-slavery forces controlled the Supreme Court by the war's end.