I already sent NDef messages between two Android devices (several Galaxy Nexus, Nexus S, 4.0.1, 4.0.2 and 4.0.3) with 32,000 bytes + NDef header. If you are really careful (do not move the device) and the patient (this lasts several minutes), this can be done with any problem.
So, the problem should not be in the Android part, but I have not tested it with a card reader.
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