First of all, FAFSA, FAFSA, FAFSA!!! Even if you're making a 6-figure income, you should still have your kids fill out the Federal Application For Student Aid.
I applaud you for saving up money to help pay for your childrens' college expenses, but if it's not possible, it's not possible, there's nothing you can do. Now let's take a look at what your kids can do. As mentioned above, Pell Grants and Perkins Loans are need-based and can provide money for college. Your kids however, should definitely go to their high school counselor and college resource center (Assuming they have one) and inquire about scholarships. Even if they don't qualify for merit based scholarships, there are TONS of scholarships out there for anything and everything.
Just an example: Dave Letterman the late-night talk show host gives a scholarship to one student each year at his alma-mater. The qualifications? The student must have a 2.0 GPA. No higher, no lower.
Individuals or companies can set whatever qualifications they like for scholarships they fund. Chances are, depending on your race, religion, field of study, extracurricular activities, street address, city, town, state, etc. your kids could qualify for and apply for numerous scholarships. Some may be merit based, and some may not be. Get them to do their homework. If you tell them that they might need to take out a loan for their own education, that provides an incentive for them to do as much as possible to get funding from someplace else besides the Bank of Mom and/or Dad.