In OTL the creation of the Republican party was not a sure thing and depended on a variety of unique conditions. What other political parties can be formed when the Whigs collaspe besides than the Republicans?
If the Whigs collapse sooner I could see a rebirth of the Liberty party, and the formation of a slavery neutral CU-esque party.
So you want, what exactly? The Republican Party under a different name? Because that is what the Liberty or Free Soil Parties being more successful after the Whig collapse is going to entail. They are going to have to try to absorb the exact same constituencies that the Republicans did IOTL following the Whig collapse and they are going to do it with platforms that are quite similar.
The most interesting alternate option is the American Party because they could stand a chance of absorbing old Whigs and retaining relative neutrality on the slavery and sectional issues of the time. Many of them were absorbed IOTL into the Republican Party so you still have that difficulty to deal with, but they could be sufficiently different to merit discussion.
At the point of the Whig's collapse, most chance of compromise is dead, however. The Democratic Party has swung too far to the side of slavery and compromise on the part of the North is viewed as treason to many on the South. For this reason, most attempts to bridge that divide (such as a Constitutional Union parallel) are doomed to failure. Beyond that, any tripartite split just isn't going to last very long in American electoral politics.
No. A party based on total abolition couldn't be succesful (The Republicans in 1860 ran on a platform of ending slavery in the territories, not the south/border states).Would they be electorally successful?
What if the Democrats permanetly splinter?
They won't any more than they did IOTL. And I repeat, any tripartite solution is untenable at best.