I think you can withdraw your application and get at least a partial refund. You might want to investigate how much you would get back if you withdraw your application. Given your limited evidence, it may be your best alternative at this point. Then collect the necessary evidence to make a sound and compelling case and re-apply. But you should definitely read the OP2 manual I gave you the link to before you attempt to reapply or submit more documents. You seem not well-informed about the process and it is quite expensive to apply and get refused just for lack of including appropriate evidence.
The burden of proof will be high if you are refused and then apply again. You will have to overcome the problems with the first application. The burden of proof is also a lot higher for common law applicants than married ones. You must provide irrefutable evidence of living together at least one year. In addition, you must prove (like married couples and conjugal partners) that you are in a marriage-like interdependent relationship. A list of the types of evidence can be found in the OP 2 manual.
If you are going to go ahead with your application, you are going to have to find some evidence (of your living together AND your relationship) or your will be denied for sure. It is time to get creative in your thinking! Ask his mom, the co-signer on the property make a statutory declaration of your living arrangements, specifically stating how long you have lived together.
Ask your friends to re-do those letters and include details of how long they've known you, how they came to know about your relationship, what they know about your living arrangements and how long they've known it. Ask them to state that they believe you are in a marriage-like relationship and to give examples of how you present yourselves as a couple etc. Get them NOTARIZED (at least 2 of them). How about people from work? Can your boss or co-workers attest to your living arrangements? Also, consider asking neighbors for the same. Any external documentation (meaning not originating from you or your sponsor) will help prove your case.
Are you receiving any mail at the residence? US bank statements, car insurance, pay checks, credit card bills, phone bills, anything with your name (or both your names) on it?? If so, trace those back as far as you can (hopefully at least one year from the date of your app) and include those. Pay to get those back statements if you have to, but get them.
Are you contributing to the mortgage? If so, are you paying by check? If not, get your spouse (or his mom) to write a letter stating what you contribute and for how long. Show the monthly deductions from your account. What about groceries and other regular costs of living expenses...who pays and where?
Photos, cards, letters, gifts, and emails from friends and family? Facebook postings? Anything from before you were living together? Ask friends and family if they have pictures of you and him with each other's friends and family, at special events, etc. Include those. You have a child together? Where was the baby born? Who paid the medical bills? Who's insurance covers the child?
That is all I can think of for now. You might want to post in the Family Class folder. Explain in detail your situation, what you've already provided as evidence, what evidence you are being asked to produce and your timeline for getting these documents back to the VO. It is a very active folder and I am sure others will think of things beyond what Kelkel and I have posted here.