You can indeed petition for a reduction in your support amount. Get the required forms from your local courthouse as soon as you possibly can and file for a reduction. Some judges will grant them and some won't. Don't get your hopes up- a lot of judges won't care why you can't pay, no matter what the reason.
As for keeping your job loss from becoming a strike against you, maintain an active search for employment and document every effort or application. Be able to show that you're actively (even vigorously) seeking work.