I came to the US under the visa waiver program, I overstayed about 10 months because I couldn't afford the fees for the adjustment of status after getting married to a citizen, am I going to need to fill up an I-601 form after applying for the adjustment?
You might be able to adjust status without needing an I-601A or consular processing, but it will depend on your local USCIS office's protocol. Some offices view Visa Waiver Program overstays like any other overstay and allow for adjustment of status. Other offices (e.g. San Diego) view the VWP overstay as ineligible to adjust status. From my experience, most offices are okay with VWP overstay adjustments, but you'll want to make sure you use an immigration attorney that can say they've handled a VWP overstay adjustment in the Louisville (or wherever you'll process) USCIS office, and it was approved.
You won't necessarily need the form unless grounds of inadmissibility apply. The article below touches on VWP adjustments.
Kindly note that this posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Remember, this site is akin to an internet blog. Do not rely on information here to make important decisions in your life. Make an appointment to meet with a licensed attorney in his or her office (or via Skype or phone) to obtain competent personal and professional guidance.
Hire a lawyer
Ask him/her to have an I-601 prepared ...which can be submitted if the officer insists.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.