History question, re: Freedom Riders and the Kennedy administration

My oldest daughter is in 8th grade and is receiving a visit today from Congressman John Lewis of GA and CT Vivian, both original Freedom Riders during the civil rights struggle. Very cool, I wish I could be there - They are going to talk about the Freedom Rider movement that forced the issue of integrated public buses in the South, which was resisting federal law to maintain the status quo.

Each student will be allowed to ask one question. I asked my daughter what she planned to ask and was impressed by her response. She said she learned that the Kennedy administration turned a blind eye to the Freedom Riders at first. John barely acknowledged it and Robert, as US Attorney General, issued a statement condemning the FRs. They both eventually came around but it took a while. She wants to know why the Kennedy administration was so slow to get behind them. I told her I wasn't alive then, and that frankly I didn't know. I told her based on what I know of JFK, it was likely there were external political variables keeping him from engaging the issue properly. I also told her it was a good question and that she should ask it.

So the question is, to any DUers who were alive and politically aware during that period, why did John and Robert take so long to come around? I've googled it a bit, and the lag period by the administration was indeed there, but there's a not a lot to suggest why, except for one oblique reference to the Bay of Pigs fiasco and how JFK was still recovering politically from it. Perhaps that's it. Were the Kennedys constrained politically, personally, or what? Anyone remember?