Should be in line for a drafting/design position with the possibility of checking submittals/doing construction admin. We have several folks doing that here with lesser associates degrees. 

Do CM you will make a lot more... plus a lot of CM B.S. degrees allow and are tailored around working while doing it in the field if you wanted to finish it up. The guys I went to school with in CM (I did a dual Arch-CM undergrad ) started at 55k+... I went to graduate architecture school paid 107K and still make 51K with 5 years exp.

I did a professional Arch degree, I then took a CM course at a community college and met the associate architecture majors. You guys are better trained than the 4 year and master programs. Go into interviews and network with confidence by saying, " I actually know how to draft and how to set up construction sets." The community colleges are treating it like a vocational training and are setting you up to get a job. The universities are treating it like a philosophy major. You have better training, trust me.

I am unsure how long you have been in school. I started off in a community college and transferred into a university and finished with a B. Arch. My parents did not pay for college. I worked full time and went to architecture school full time and managed to get out with only $65,000 in loans. It was painful but I managed. Don't let your families lack of wealth set you back. If your parents are poor, you can get financial aid(which means you won't have to work as much), and if you don't get aid, you can get government/private loans to assist with what you can't cover by working but you will need to work and go to school.

If that sounds like too much, then choose either the Associates in Architecture and then move on to become a drafter in an architecture firm and move up from there, or choose the Associates in Construction Management and move on to work towards a position as a project manager for a general contractor. Whatever you do, don't do both! I know that both will take you 4 years. If you are going to invest that time, do a full degree! 

If money is what you are after, choose the construction management associates degree. Look up the salary of a construction estimator, construction project manager and architectural drafter so you can get your head around it. If you care passionately about design, then choose architecture, but be prepared to be paid less. Don't let the fact that you came from a poor family paint you in a corner. People rise above and go to school all the time. I was one of the few in my program who worked and went to school. I worked full time and attended architecture school full time. I barely slept but I made it happen. I am still paying for it, but now I can go onto a Master Program if I want and will always have that education with me.

If you can, try to get a job running errands in a construction company or architecture firm and get your foot in the door. Some companies will help pay for you to do your schooling. 

"All our dreams can come true, if we have the courage to pursue them." -Walt Disney

what college is it that is offering construction management program?