Politicians were unable to find a political solution to this crisis because the enmity between the North and the South had gone to far to be resolved. There had been all sorts of political solutions that had been tried in the past and now there were simply no more solutions that had much of a hope of solving the crisis.
The history of the United States for the 40 years before the secession was one of compromises and political solutions between the two sections. There had been the Missouri Compromise and the Compromise of 1850. There had been the Kansas-Nebraska Act. Things like these had been tried as ways to find a political solution to the sectional issue.
By 1861, there were no more ideas. Compromise had been tried and had failed (and the Dred Scott case made it harder to be able to compromise). The degree of animosity between the two sides (built up over at least 40 years) had also increased to the point where political solutions were impossible.
So the politicians couldn't find a solution because A) the two sides hated each other so much and B) all the good ideas for solutions had been tried and had failed.