In my experience AMEX payments done online or via telephone hit my bank account as "pending" on next day, with processing taking place on whatever following business day. That is if make payment today before 12 midnight it will show as "pending" sometime on Sunday, and funds withdrawn as part of Monday's work.

IIRC AMEX is actually a bank, and thus can process payments rather quickly, more so thanks to modern bank processing (Check21) rules.

Believe AMEX will make two attempts to process an online or telephone payment that isn't honored by your bank before giving up. Not sure if they charge a return fee and or otherwise have adverse reaction against account between those two successive attempts.

If for any reason your account is short funds to cover AMEX or whatever payment seen as "pending" go to your bank at once and make a cash deposit to cover, then speak with a customer service rep either at branch or telephone. Banks have "over draft" departments or officers that handle these things, basically deciding if something that will over draw an account will be paid or returned. If you make a deposit before a certain time and let bank know the money is there, they usually will pay whatever is coming in that would cause over draft. You might get dinged for an OD fee, but that is better than AMEX or whoever you wrote check/made payment to doing same.