Can I cross the border with my children without a pport and authorization letter to travel with my children?

I am going down to mexico in 1 month and I was wondering if i can walk across the border with my children if we don't have pports. My husband was deported 4 years ago and we never got pports. Our children and I are us citizens and want to finally reunite with my husband. He would be waiting for us across the border as close to the gates as possible but I am worried that they won't let us in the country without doentation. All I have is our marriage certificate and the birth certificates for the children. Obviously it states that their father was born in Mexico so I am thinking that shouldn't be a problem and if there was a problem could he just wait by the gates and show his ID an give consent that way. If anyone knows how it works on the border for children crossing with only one parent i would greatly appreciate it. Thanks.