I have bench warrant issued for littering. Am I going to jail?

This was about a year ago for a littering violation. I threw a cig out of a car. I showed up to court and they gave me a date to meet with the judge. After that, my fiancee got pregnant and was in and out of the hospital so I missed my court date and was issued a bench warrant. What is the penalty if i go to court? I don't want to go to jail because I am the major source of income at the moment for the family and I watch the baby on the weekends. Is jail time mandatory? Can I pay this off? Do I have to go in to court to resolve this? I'm scared they will make me stay and I end up getting fired. If it helps, this was issued in California by the LAPD. Do these warrants expire?