I'm not sure I understand exactly where it broke....but there is a "pull" cable and a "push" cable. You really ought to have both seeing as the pull cable is what is normally used to open the throttle. I assume your push cable broke since you aren't experiencing problems with throttle operation. You really ought to have it though like I said, it is a safety measure. If the pull cable breaks then the throttle will stick open (without a push cable) and could cause an accident, etc. If you have an operable push cable then you can rotate the throttle closed and close the throttle body, slowing the engine to idle.
Bottom line, definitely fix it, it shouldn't cost much (just a guess but maybe $25-$50) and shouldn't take more than 30 to 60 minutes to replace. Well worth the time and money to possibly save your life at some point. JMO...
Also, if you lube your cables every time you change your oil you will never have to replace them.