The other answers are very good. The lawyers for Child Support Services handle contempt charges every week. It is just another day for them. It is not personal. If you think you have a valid defense, simply ask for appointed counsel. Although a recent US Supreme Court case gave a slight opening for the court to refuse to appoint counsel in a civil contempt context, I have never heard of such a thing in California. In fact, a pilot project in this state is currently expanding the use of appointed counsel. If, for some reason, you are denied appointed counsel, certainly come back and ask for alternate strategies, but I would be really surprised.
Then explain your defense theories to the appointed attorney. Some might fly, but others might not. For example, an order is not invalid just because it is inequitable. See Family Code section 3692 (http://law.onecle.com/california/family/3692.html). Caselaw has also held that you can't collaterally attack an order through a contempt; rather you must use the appropriate legal process (set aside/appeal). A case that I would expect the prosecutor to cite is Stone v. Bach, which is very strong on this point (http://188.8.131.52/leagle/xmlResult.aspx?page=1&xmldoc=197852280CalApp3d442_1491.xml&docbase=CSLWAR1-1950-1985&SizeDisp=7). Fraud is also likely to fail as a defense to a contempt, although it would be a valid reason for a set-aside (http://law.onecle.com/california/family/3691.html). Inability to comply is a solid defense if you were actually unemployed, but if not, expect the prosecutor to hit you with Family Code section 4011 (http://law.onecle.com/california/family/4011.html). Yes, you read that correctly....it says payment of child support is a legal obligation that supercedes even your rent. If you had enough for your rent, but you didn't pay child support, you've got a problem. The fact that you have a fee waiver makes me suspect you have a defense on inability to pay grounds, but your attorney will need to look at the facts.
But, even if a perfectly solid defense is not there, still seek counsel. He/she may find something. Also, most family law lawyers have a relationship with the local department of child support and they may be able to work out a negotiated settlement that may be very acceptable to you.
On seven counts of contempt the maximum penalty is 120 hours of community service or five days in jail per court.
Because the total amount of possible jail time is less than six months you are not entitled to a jury trial.
You need to appear at the hearing and request an attorney be appointed to represent you. Anything you file in court could be used against you so you should really talk with an attorney before you do anything.
There are very few defenses to nonpayment of child support. You need to discuss those defenses with an attorney.
You need to get a competent attorney appointed to represent you. This isn't a "contest of the wills" at this point, even though you think it is; it's an effort to keep you out of jail. A competent defense attorney is much more likely to be successful in that goal than you are.