Thank you for contacting me about your Tax issue. I will work hard to help you understand the issue clearly.
It is still 2013 and your employee(s) in IL need to have their earnings reported to IL and have IL taxes deducted for 2013. There is still time to do this.
The penalties to the state of IL are likely to be minimal, but you likely will out state unemployment in arrears.
You will need to register with IDES (State employment commission) as soon as possible: http://www.ides.illinois.gov/default.aspx
I would NOT recommend waiting to 2014 to do this.
In addition, if your business operates in IL, you may wish to register in IL as a foreign LLC.
Information about IL LLC's can be found here: http://www.cyberdriveillinois.com/departments/business_services/limited_liability_companies/home.html
Your LLC will still be based in Texas, but it will have a foreign registration in IL. You will likely be liable for IL state taxes starting in 2013
So, do I file the earlier quarters of 2013 late for employee income tax and wait for an interest and penalty notice?
I don't understand the phrase "but you likely will out state unemployment in arrears."
What tab under Illinois LLC would direct me to "foreign LLC"?
Yes, you will need to catch up with the earlier 2013 quarters. Since you are in the 4th Q, you are not late there. The 3Q reports were due only 3 weeks ago.
That phrase above makes no sense to me either. You will have some penalties for late payment and filing, but it should not be an overwhelming amount. Sometimes you can ask for penalties to be abated on the first time.
You may wish to seek advice of an IL attorney regarding registration requirements in IL, but this form: http://www.cyberdriveillinois.com/publications/pdf_publications/llc455.pdf is typically used to register your foreign LLC in IL.