Yes, in most all states failing to comply with a traffic ticket by either paying the fine, showing up at traffic court or complying with a citation in another legal way can lead to a suspension of your license.
To not pay more than one ticket you are likely looking at a lengthy suspension as well as high fines and late fees. The penalty for not taking care of a speeding ticket, or multiple tickets, will differ upon state laws of the area in which you were ticketed.
For example in Connecticut's court system states that you must respond by the Answer Date on your ticket - the Answer Date is assigned by the police officer who issued the ticket. If you do not pay in full or plead Not Guilty by the Answer Date, your case will be transferred to court.
If your ticket is for a motor vehicle matter the Department of Motor Vehicles will be notified that you have failed to pay or plead Not Guilty. The DMV will suspend your driver’s license. You will be required to pay a reopening fee of $60.00 to the Clerk of the Court where the ticket was issued, in addition to the original amount due. You may also be required to pay a $125.00 fee to the Department of Motor Vehicles to have your driver’s license reinstated.
If your ticket is for a non-motor vehicle infraction and you fail to pay in full or plead Not Guilty, your case will be transferred to court, an arrest warrant will be issued, and a bond for your release may be set by the court. This will add the charge of "Failure to Pay or Plead" to your original charge.
Other states have similar laws. For a second example the courts in Pasadena, California list the following for those that do not pay their traffic tickets on time:
Failure to appear or failure to pay fines may result in (1) Denial of renewal of your Driver’s License (2) Denial of your renewal of your vehicle registration (3) The filing of an additional charge of Failure to appear and the issuance of a warrant for your arrest.
So contact the court or your states Department of Motor Vehicles to find out if your license has been suspended due to nonpayment of 3 speeding tickets and what you need to do to correct the situation and get your license reinstated.