A significant portion of every class takes on some form of financial aid, so you certainly will be in good company. An MBA is an expensive proposition, and fewer people will have the "cash position" to pay for it at once without some form of assistance.
If you haven't had a chance to do so, yet, check out http://www.wharton.upenn.edu/mba/admissions/financing-your-mba.cfm and http://www.wharton.upenn.edu/mba/admissions/financing-your-mba-faq.cfm.
Now, to answer your question, it is possible that you may not receive the total amount of aid you seek or need. Each applicant would be assessed on a case-by-case basis. If you end up not getting the amount of aid that you sought, you have at least three options:
a) you could pursue other external sources of aid or merit awards;
b) you could reinvestigate whether or not you are willing to take on more loans/debt;
c) you could *maybe* defer admission - with a compelling reason - and try to return the following year after saving more money; or
d) you could decline your acceptance to Wharton.
I suppose theoretically you could appeal to the Financial Aid office if you have a very compelling reason to do so (just saying I need more money will probably not work, as the Financial Aid office will already have evaluated your profile, if and where applicable). But I would not count on this option.
In any event, I would discourage you from giving up at once until you have further explored options, perhaps in conjunction with the Financial Aid office.