I'm not sure which broker you're using, but some of them work over the weekends as well, so it won't be just sitting there. If you're concerned then call and ask how they handle weekend submissions.
If using TTS go ahead and fax ASAP. They have Saturday and Sunday hours. They were also kind enough to send us an email once they received our faxes, etc. Good luck to you!!
Most large companies are using electronic fax servers these days. The faxes are electronic and are not spitting out the old fashioned way on paper out of a printer.