A straightforward spring replacement or roller swap is usually a single visit, start to finish. Track realignment runs about the same, assuming the bracket mounts underneath haven't rotted out, which does happen on houses old enough to have had a roof or siding job or two since 1963.
Where it slows down is parts. If your door is still running on an original or near-original track width that newer doors don't use, or an opener model old enough that the drive gear is no longer a stock item, we may need to order the part rather than carry it on the truck. We'd rather tell you that upfront than promise a same-visit fix we can't deliver.
We don't quote a fixed response time for Hamden specifically, since the truck is coming from New Haven and the day's schedule varies. What we can say is that once we're on-site, most single-fault repairs don't turn into multi-day jobs unless the part itself needs ordering.