So I had the same issue.  I spoke with customer service at EFTPS and she was very helpful and helped me.

I too had changed my password.  Then come to find out that the password was too long for QuickBooks.  (I think that there should be better notification to the maximum of 12 characters for QuickBooks- and the minimum for EFTPS is 12.  So all passwords should be ONLY 12 characters.)

Anyway, she helped me change my password for the second time today.  I didn't have to wait the 10 days.

Make sure you are LOGGED OUT.

You go to the log in screen of EFTPS and click on change my password. (down under all boxes) 

1. enter EIN

2. enter PIN (4 digit given by EFTPS previously)

3. enter last 8 of enrollment

then continue

will bring up screen for create new password.

Create you 12 character password -(she did tell me that the special character has to be at the END)

Once you enter this and it goes to the next screen saying it has been changed.  You have to click on the "login" in the message.  This will take you to the login screen and you log in using the new password.  Once that is done then the password is actually set.  If you skip this step it doesn't set your password.

I was then able to go and pay my payroll taxes and input the newly created password. No issues!  She was a miracle worker!