The Constitution Union Party (also known as the Bell Everett Party) was made up of former Whigs, Know-Nothings and a number of Southern Democrats. The party drew its name from its simple platform "to recognize no political principle other than the Constitution...the Union...and the Enforcement of the Laws." Their hope was that by not taking a stand for or against slavery or the expansion of slavery, they could side steps whole issue.
Senator John J Crittenden of Kentucky set up the meeting of fifty conservative, compromise seeking Congressmen in December 1859. This meeting brought on the convention in Baltimore, Maryland on May 8th 1860, one week before the Republican convention. They elected John Bell of Tennessee as their Presidential candidate and Edward Everett of Massachusetts for Vice President.
The Constitution Union Party only won the electoral votes in three states, Kentucky, Tennessee, and Virginia. The only non-slave holding states to give the party more than 5% of the votes were California and Massachusetts. The party disappeared once the southern state began to secede.
If you’re interested in the platform of this political party, this web site should help; Constitutional Union Party Platform of 1860