Should I give it a try or not to fix his immigration papers since he entered this country illegally?

If he entered the US unlawfully, under the current immigration laws, he is not eligible to adjust his status within the US. He would have to go back to Mexico but as soon as he leaves the US, he automatically triggers a 10 year bar to reentry, which can only be waived by a showing of extreme hardship to a US citizen spouse, which is fairly difficult to do in most cases.

You may petition for your husband but he will need a waiver in order to be admitted to the United States. He will not qualify for the provisional waiver I-601A because he has been convicted of a DWI. You may still qualify for the traditional waiver but that will have to happen in Ciudad Juarez and could take 1 year to get a response on the waiver. I would strongly suggest that you sit down with an experienced Immigration attorney and see your options today and would look to see what happens in the near future with immigration reform.