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