illegal immigrant marries a natural born us citizen

I would recommend consulting with an experienced immigration attorney to review the immigrant's immigration history before preparing an adjustment of status application. This is definitely one of those situations where I advise my clients not to do it on their own. The illegal immigrant may or may not be eligible to apply for immigration benefits regardless of the marriage to a US citizen (with child) or at the very least will likely require a hardship waiver filing, or possibly appearing before an immigration judge. Be sure to bring all proof of both spouses' identity and nationality and proof of continuous physical presence to your initial consultation. Best of luck!

Your question leaves out many facts that are necessary to assess whether you are eligible to apply for permanent residency. Thus, it is critical that you seek the counsel of an experienced immigration lawyer.

However, in many instances, I would generally advise for a United States citizen spouse to go ahead and file a petition for alien relative. Thereafter, depending on the individual's situation, one may consider adjustment of status or consular processing with hardship waiver. If neither are viable options, I would notify the National Visa Center to hold the approved petition in abeyance. You could then wait for possible changes in the law and then seek to continue with your immigrant process.

Given the number of variables in this case, please consult an immigration attorney at your earliest convenience to lay out a long term strategy.