Update: It turns out that thanks to ING-Direct I was able to fund my (non Citi) bank account today (the due date). So, I went to citi.com and tried to use the click-to-pay feature. To my horror, the CTP only allowed me to pay $1000!! Of course, being a miles fAAnatic, my balance was huuge. So... I just paid the $1K online, and then rushed to the local branch to pay the rest by check, just minutes before the 1pm (ET) deadline. The teller (a hottie, BTW) told me that the payment would post right away. My concern was first, to avoid paying a late fee, and second, to avoid paying interest by carrying a balance.

Thanks for the replies!!