My A/C is not blowing cold air anymore

My air conditioner is blowing warm air and my speedometer is falling below the 0 mark gear on neutral. Mechanic said the problems are related. Is he right? Speedometer needle is under showing actual speed and air conditioner air is not cool as it should be. Often there is a clicking sound from under the hood, which leads me to think its a thermostat problem but my mechanic says the air cond problem is caused by the faulty console with the speedometer. Please advise me before I am asked to spend a bomb to replace the whole console.