If someone is saying these things after a couple of dates, they are just being a bit rude about not being interested, along the lines of what lilypup suggests. What's too much drama or too intense for one person may be fair game for another.

If I called someone intense, it would be because they seemed very focused and/or fixated on something.

Kaliope's definition of drama seems pretty accurate. It could also be just that someone takes small problems too seriously (which we have all been guilty of!).