If you're willing to forgo gifts, then ask your guests to bring a potluck dish instead. You can group guests into categories (main course, salad, etc.) or ask them to provide a themed dish that reflects your personality as a couple. Make it fun, and not only will it alleviate your budget woes, but it will also make your wedding an event to remember! You can offer an open bar in return.
Photo by Couture Events via Style Me Pretty