A furnace that fires, runs for a minute or two, then shuts off — and repeats — is short-cycling. The most common cause in Sacramento is a dirty flame sensor. The sensor confirms the burners have actually ignited; when it's coated with a thin layer of corrosion, it loses the signal, the control board assumes no flame, and it shuts off the gas valve as a safety measure. Cleaning the flame sensor with fine steel wool takes five minutes and fixes a large fraction of short-cycle complaints.
A severely clogged air filter causes the same symptom through a different path — heat builds up because airflow is restricted, the high-limit switch trips, and the unit shuts down. Change the filter and run the system.
A failing high-limit switch, a bad pressure switch, or a cracked heat exchanger (which can affect the pressure-switch circuit) will also produce short cycles. A cracked heat exchanger is a carbon-monoxide hazard and changes the conversation to replacement, not repair.
Less common but worth mentioning: a furnace that's oversized for the home will short-cycle by design. The home reaches temperature faster than the burner can complete a proper heat cycle, the thermostat satisfies, and the unit shuts down. This isn't a fix so much as a sizing mistake from the original installation. If your furnace is new-ish and always short-cycled, that may be why.