Well, I do a ton of single-member LLCs here in Tennessee...been in practice for many moons, and i have yet to have a single-member LLC WITHOUT a FEIN.   Been a ProSeries Professional user for long before LLCs were even created. I don't know where you get your 'many users' from, but obviously not in my part of West Tennessee. 

One solution, the obvious one, is that in the time you took to type this question, you could have applied for a FEIN, printed out the CP-575 A for your records, and filed the return.

I've been trying for 3 years to get them to fix the 'automatically requiring F & E estimates' (no matter if the tax liability is $100 or any amount under the $5,000 threshold where estimates are required).