One way to move that balance is to bribe some of the powerful people who are on the fence, or close to it. (For instance, people who are starting to see the moral case, but are also pretty concerned about their 401k, or its 18thC equivalent.) Of course this bribe was tempting to those pushing for change, they could have victory now, instead of waiting another generation.
On the other hand, attaching to the bill to free the slaves a huge bill to pay them each compensation, this would clearly push the balance the other way, and thus delay the date until it could get a majority (of those with the relevant power).