Can too many credits force you to graduate early? I'm about to enroll at a local university as a mathematics major, with a view to later transferring and studying engineering.

I can receive enough credits through AP, CLEP, and credit by exam to cover 1-2 years of study.
However, I'm unsure of how many years I would like to study at university.  Likely 3-4.  Could receiving enough credit for 2 years hurt my chances of being able to transfer and spend 4 years total at university?

I'm relying on federal grants and state and university scholarships to fund my study; could those be withdrawn if I have enough credits to graduate but choose not to?
Yes, this is a potential concern, particularly with regard to financial aid.

US financial aid sources are commonly restricted to be used only for education that is leading toward a particular degree.  You can't take random courses indefinitely and expect the government to keep paying for it.

My institution's financial policy has the following clause:


  Only course work that is required for my degree will count towards my enrollment status. Once I complete the requirements for a single degree, even if I haven't applied for graduation, I am no longer eligible for aid for that program. The fact that I might be getting a dual degree and haven’t completed the requirements for the second degree doesn't change this. 


Sometimes this can be "gamed" by completing the actual degree requirements very slowly while taking lots of other courses in the meantime; but there are likely to be limits in place.

You should discuss your plan of study carefully with both an academic advisor and a financial aid officer at the university you plan to attend.  (The academic advisor might not be an expert on financial aid details, and vice versa, so it is important to consult both.)