Seward had more enemies than Lincoln (which is why Lincoln got the nomination), but I still think the Democrats would have split and that a Seward ticket would have prevailed.
Cincinnati editor Murat Halstead was at the Charleston convention. After the Deep South bolted, he heard lots of "rampant Democrats" and Southerners speaking of Seward's election as a certainty. Many even said they thought Seward would be a good President - though with (IMHO) the tacit assumption that the South would secede if Seward was elected.
When you crunch the 1860 numbers, you find that even if all the Douglas, Breckinridge and Bell votes had been for a single candidate, the Republican ticket still would have won.
Well, yeah, obviously, but no one has ever suggested that if Seward was nominated there would be a single opposing candidate. The ex-Whigs would still nominate John Bell in hopes of avoiding secession, the regular Democrats would still nominate Douglas, the southern Democrats would still nominate Breckinridge.
The question is whether Seward would get all the votes Lincoln got; and if not, what states he might lose and to whom. Many Republican leaders thought Seward could not win Indiana or Pennsylvania, and Illinois was doubtful too. (Lincoln won there fairly narrowly, even though he neutralized Douglas' native-son appeal.)
Oregon and California were really split; the fear among Republicans is that Seward's radicalism would shift many ex-Whig votes to Bell. That could easily throw California to Douglas and Oregon to Breckinridge.
All these changes could drop the Republican electoral vote count by 60 or more, to far less than a majority. However, it would still be unlikely that anyone else could get a majority, throwing the election into the House with all sorts of bizarreness.