"Can they back out like this"
*** Based solely on the information in your post, they can't back out unless you let them.
"or delay on this ?"
*** Of course they can delay. Send them a certified letter RRR demanding to know there promised completion date. If they still refuse or fail to respond, take them to court.
It would appear in a cursory review of NC statutes, that what the dealer did was in violation of the following:
"§ 20-342. Unlawful devices.
It is unlawful for any person knowingly to advertise for sale, to sell, to use, or to install or to have installed, any device which causes an odometer to register any mileage other than the true mileage driven. For the purposes of this section, the true mileage driven is that mileage driven by the vehicle as
registered by the odometer within the manufacturer's designed tolerance."
Most odometers are connected via the speedometer. If this is the case in your vehicle, the non-working speedometer would affect the odometer..... and thereby cause a violation of the above.
Also:
"§ 20-123.2 Speedometer.
(a)Every self-propelled motor vehicle when operated on the highway shall be equipped with a speedometer which shall be maintained in good working order.
(b) Any person violating this section shall have committed an infraction and may be ordered to pay a penalty of not more than twenty-five dollars ($25.00). No drivers license points, insurance points or premium surcharge shall be assessed on or imputed to any party on account of a violation of this section."
Source for the above:
http://www.ncga.state.nc.us/statutes/generalstatutes/html/bychapter/chapter_20.html
It is also very likely that the dealer who sold this vehicle with the non-working speedometer is in violation of his licensing regulations. To find out if this is correct and to file a complaint, contact the NC DMV at:
http://www.dmv.dot.state.nc.us/enforcement/offices/districtoffices.html