I found a work-around, based on a theory...
As I understand it, the DCN is an IRS-assigned value. It is only assigned/received when the IRS accepts the efiling of the federal tax form.
In my case, I e-filed the federal form a day before I attempted (and failed, due to this "DCN has too many characters" error) to e-file my state.
It only took the IRS about 20 minutes to accept my e-filed federal copy. At which point, I think I was hosed. The DCN assigned by the IRS is too long to fit into whatever (invisible) blank in the state form TurboTax wants to fill in. And thus the error.
The workaround? Painful: open a new turbotax file from scratch. Re-enter all your data. Compare the data carefully with your first one. (I printed PDFs from both files, and compared, and iterated.) Then, using the new file, e-file only to the state. It worked, at least for me...
