Absolutely NOT - springs are replaceable without removing the door. Note, however, that unless these were new springs and one failed prematurely, the springs should be replaced in pairs, otherwise the door will open "stronger" on one side than the other, resulting in racking and more wheel friction, eventually leading to cracked door panels and damaged opener.
You can check the Home > Garage Door link right under your question for more info on cost - generally about $25-65/spring, plus about $75-125 installation cost for a total of generally around $125-250 total cost.
Search the List (ingreen banner bar above) for local Garage Door specialists and their ratings and reviews. Here is a link to another post with prior responses (one is mine) that might help too -
When you call for service, be prepared to tell them the following things so they have a better chance of bringing right parts on first trip - type of door (swing out, tilt up, panel type roll-up, corrugated metal rollup), door materials (wood or metal), door width, # of springs on door (1 or 2), door manufacturer if you can find it on door - usually on edge of panels, or on plate right next to lock (but NOT the name on the lock itself, nor the name on the opener).