Currently on H1B and employer wants to start the green card process.
The time frame to complete the entire GC process (i.e. filing of PERM, I-140, and AOS) for EB-2 preference category will depend upon your country of birth. PERM and I-140 can be completed within 9-11 months (if really pushed), but the timing of filing for AOS will be governed by your priority date and the country of birth. If you were born in a country, other than India and China, I would say you have a pretty good chance to get the GC in 16 months, assuming priority dates don't retrogress and the USCIS keeps the rate of adjudication consistent.
Too many variable to be able to provide a timeline.
Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.