Its more that Lincoln had most of them since 1861 and did good work to keep them on board through appointments and through changing the name to the National Union Party for 1864.
Thus it was more that McClelland failed to gain many of them back and a big part of the reason was the split within the Democratic Party between those who supported the war and those who supported the copperheads.
The Democratic Party organization was very much dominated by copperheads and they composed a copperhead platform even while nominating McClellan.
So would this below analysis be correct in your view?:
"Soft" War Democrats supported McClellan as they found his pro-war views satisfactory enough to stick to their old party. Although they were pro-war, they were not so hardline on that issue that they felt it worth abandoning their party just because the party organization itself had suspicious copperhead tendencies, they trusted McClellan enough to believe he was his own man on the issue.
"Hard" War Democrats supported Lincoln because they trusted him due to already have been doing the job for 4 years. They found the copperhead dominance of the Democratic party suspicious, especially since the VP nominee was a copperhead themselves. Lincoln was a proven figure they trusted to fight the war with full passion in spite of their disagreements, while they were not confident that McClellan would fight it with the same vigor due to how his party would be influencing him to be a dove.