How urgent is it to fix cracks in foundation?
Small hairline cracks are fairly common in foundations and slabs. They are usually caused by ground subsidence, and typical freeze/thaw cycles. They can also form almost immediately after the slab is poured for various reasons. If the crack continues to open, or there is any shift in the slab, you definitely would want to get it checked out by a professional.

Slabs can be very costly to repair. There are techniques out there such as slab jacking, and underpinning the foundation. These kinds of repairs can be in the tens of thousands of dollars.

Honestly, this sounds like a scare tactic from your contractor to drum up some business. If I were you, I would first fill the crack with a caulk made to fill cracks in concrete, and keep an eye on it. If a full Winter season passes, and there is no change in it, then it should be stable enough to leave it. Just be sure to check it periodically, and inspect for other cracks.