Ok this sheds some light upon the question. It would help if we knew who the "He" is that this statment is refering to, so that we could make a comparison of his politics. But it sounds like to me that an "Unconditional Unionist" was a person who would accept the continuation of Slavery IF the Southern States would rejoin the Union.

If this is the case, then Lincoln did have a problem. Because most of these delegates were unconditional Unionist and "Freeing the Slaves" would have been a secondary concern to them. And these persons would only support such a policy if it could be shown to them just how it would reunite the Union as an overall objective in the end.