Will my car be at risk in a debt settlement program?

That is highly unlikely to happen.

They would have to sue you first and get a judgment. Then they'd have to file for an attachment on either of those vehicles. A) those vehicles would have to be paid off and you would have to have clear title. B) Your state probably has some sort of exemption for personal vehicles (IL exemption is $4500 I believe) -- which means the vehicle has to be worth more than that exemption amount in order to be attached.

Credit cards rarely go that route. If they get a judgment, they'll try to garnish your wages well before they try to take misc property that you own.

And what it I don't show any income?

I find it striking that you use the word "show" instead of "have". One might take that to mean you have income, but wouldn't reveal it. Keep in mind, they can get a citation and you would have to answer under oath that you don't have any income, and if you lied about your income in court then it would be contempt/perjury.

Other than that, if you don't have income, then their pursuit depends basically on 1) how much effort their attorney will put into it and 2) whether it's economically feasible for them to keep pumping money into the matter in hopes of collecting.

For example, I have 2 attorneys that I use (well, actually I use about 8 attorneys, but the other 6 are corporate counsel and don't actually file lawsuits). One is a "collection" attorney (that's all he does, is sue people over defaulted accounts). I consider him lazy; he only wants easy accounts where he can go into court, get a judgment and wage order, and get paid. Other than that, he won't put effort into discovering assets or other supplemental proceedings -- he'll just send me a letter back and basically say "sorry, I can't do anything else". And so I only send him easy files that I know where the debtor lives and works.

My other attorney, on the other hand, has fought cases in front of the supreme court. He really doesn't like to do "collection" cases, but he does them as a favor to me for giving him other legal matters. He gets "down and dirty" so to speak, and he'll put the extra effort in to get paid -- he'll go in to discover assets, get subpoenas for information, file for attachment, etc. (From time to time he'll even get a bench warrant for arrest, which a cookie-cutter firm probably would never consider). In other words, he puts a lot of personal involvment and attention into the matters I send him.

So you see, to answer your question, it depends what kind of an attorney your creditor is using to sue you -- a "cookie cutter" law firm, or a "real" attorney? The cookie-cutters file hundreds/thousands of cases per month, and so they can't really put a lot of time or effort into their cases -- ie they really aren't going to dig for your assets. To your benefit, most credit cards and JDB's use cookie-cutter law firms to file their cases.

I would not worry about your vehicles, it is highly unlikely that a judge would allow them to take your car away. The safest way to enter a debt settlement program is with a company who has attorneys licensed in your state, who oversee your file. They know the laws in your state and will handle things properly.
See my post on what to ask debt settlement companies.
http://www.debtconsolidationcare.com/settlement/right-company.html