All entries can be filed until you are ready to draw a winner. You've decided that running a contest will be beneficial to you. You may have to fund the first two or three contests that you hold on your site yourself. Or if you own a retail site obviously you can offer a gift certificate or specific product from your own shop. It doesn't matter.
People like to win things no matter the size.
Once you have held a few contests on your site and you have brought some traffic in you can safely ask for sponsors. Set a minimum value for your contests. This may depend on the contest itself and what type of exposure you have to offer the sponsor. This type of exposure is quite valuable to a sponsor. Be sure to include a link from your contest page to allow potential sponsors to contact you about donating their products for future contests.