Which furnace thermostats support variable swing/deadband?
Looks like many Honeywell thermostats have a "cycles per hour" setting instead of a deadband setting. Not exactly the same thing but roughly analogous. If your thermostat has that setting you could try changing it.

But if the cycle time is 10 seconds, I'm not sure the deadband is really the problem... even 1º should take longer than that. Do you have a hot air vent blowing directly on the thermostat or something? Or possibly some other problem with the furnace not lighting?