By early 1861 the situation had changed markedly from the peacetime of pre November 1860. By early 1861 7 states had already seceeded. Whereas before the election was anybody really talking about there being a war if the southern states seceeded?
In that context I don't believe that the northern people would have been voting for Lincoln to put down a secession of states by force. But were voting for Lincoln to keep the Union together by political means.
I do believe that the use of force come strickly from Lincoln and his advisors in the manner of Andrew Jackson and the 1832 Nullification Crisis.