Dear Felix
Your offer of help is truly appreciated at this time. If we can get our cost estimates down, I believe we should have this proposal ready to submit by the [date] deadline.
Taking you up on your kind offer, I know we will both be burning the midnight oil for the next week and a half. I really doubt that I will be able to complete this within the time limit without your help.
Thank you very much.
Regards
Lydia