Undergrad MGT Consulting Help

Hi, I am an undergraduate business student approaching my Senior year of college, and I am interested in applying to some management consulting firms (definitely MBB; as well as the MGT Consulting practices at Deloitte, Accenture, etc.). I go to a US New & World Report top 10 National Public University. My university would definitely be considered a target school for all major consulting firms. I have between a 3.75 and 3.8 overall GPA, and a 3.9 GPA for my major (with the overall Campus GPA for my University being between a 2.9 and 3.0). I have 4 internship experiences, and I have been involved on campus in several leadership roles. I am currently interning at a consulting firm that is rated well by Vault (top 40 overall, top 20 in the "prestige" category), but primarily works in more niche fields and practices (mostly financial services). It has been an excellent experience, but I want to look into management consulting at the big 3 and maybe a few other firms. The problem I have is my SAT and ACT scores. I am definitely at the lower end of what many firms would want. I received between a 1200 and 1250 overall on the SAT, but I did well on the Math section with a score of 660 (which may be important, since Consulting tends to be more analyitcal and data focused). On the ACT, I scored a 28 overall, with a 31 on the Math Section and a 28 on the English (which some people consider to be the ACT Verbal equivilant). I know these are not great scores, but I am curious to know if anyone can give me any feedback on my chances of being turned down for interviews (given the positives of my work experience, GPA, etc.) because of lower-end SAT/ACT scores. I also welcome any advice dealing with this issue.