Arming yourself with local knowledge of tuition fees at your state schools may help ease your concern. There also are many tax-advantaged savings vehicles you can begin funding immediately that provide hope for the university years. They're easy to set up and regular low monthly payments can be automatically deducted from your bank account. The money grows tax-deferred, and is taxed at the child's rate when withdrawn for school. By federal law, the funds can be transferred to other family members for education if the recipient decides not to, or can't, go to college.
Some plans limit school choice to within the state.
Fidelity has a prepaid plan that can be used in any state. There are no limits on total contributions. Upon withdrawal, the money is taxed at the child's rate. The money also legally belongs to the child when he or she reaches adulthood, which is one of the drawbacks. Distributions are free of Federal income tax.