G.V.
I deal with a lot of people in your situation. Surprisingly, some of the situations are reversed and the problem is a dead beat mother.
But back to the topic, before you make a decision on whether or not to let the father into your childs life;
1. Is he really a threat to your child's safety/or of kidnapping? If yes, there is always the option of supervised access.
2. Have you taken the time to think about what the father is feeling. Was the child a surprise? Did you two have a difference of opinion? What kid of person is he outside of the 'dead beat dad' persona? Before you judge the father for his actions, try thinking about what led the father to act the way he did. Perhaps he feels like he no longer has control of his life. Perhaps he thinks he will fail as a father. There is so much to consider.
If it helps any, and I'm not making light of your situation, I've known others in worse situations then your own.
...and on a personal note, I can completely relate. I am a single mother to a 23 month old. Her father and I argued about termination. I made the executive decision. I gave him a chance and although he and I are frequently at odds, he completely loves his daughter and proves it regularly.
I hope this helps. gv