Sure you can! You can make it in one week, if you are willing to skip some blows and whistles. You actually need just Mr. and Mrs Right, nice place to celebrate, wedding rings (which may be already in the family or borrowed or whatever) and bunch of friends to enjoy with. Yes, you still need and officiant, so your planning should start with him or her. Make sure all the paperwork is properly done, because wedding is not only about partying, it has legal consequences.
Use the power of social media, be prepared to have plenty of phone calls and delegate tasks if possible, try to focus on the ceremony and reception only. It doesn't matter if your wedding dress is not new (according to old saying you need only something new).
Top tip: keep your guest list small.
Your next question would probably be: Can I have a wedding in less than 48 hours?
Yes, this is possible, but not in all the states. Some have a law about waiting period, which varies from zero to six days. And in Florida, for instance, you need to complete a marriage preparation course before you can legally marry.
Here is a more in-depth article on that subject:
On the other hand in Las Vegas you just have to come in person and have some kind of identity card.
But before you marry on such short notice, please think a bit. Are you really really sure you want to do it?
If the answer is yes, go for it and all the best!