For us we planned everything in the year or so before he arrived, something I don't recommend doing for most people. Vendors I chose knew our situation and were willing to be okay with that - we put in nothing concrete until visa was in hand. Most states do have venues which can provide elopement ceremonies or small style weddings that can give you an experience without the hassle. I wanted a great deal of control over factors of our wedding instead of handing it off to family members that would likely run things into the ground, but usually it's important to delegate if you can. Don't be afraid to discuss options with venues and vendors, many are understanding. They want the money afterall. I used many websites like theknot and weddingwire to search for vendors that I needed.
Still there were problems:
1) I had my wedding dress long ago and the hardworking ladies in the back got it looking great in time. The problem was everyone else's outfits had to be ordered. The company claimed they had ordered months ago, but when time came to collect the orders went missing. My MoH's gown ended up having to be the last one on the rack that had damage, but the ladies got it fixed in time.
2) Our venue of choice had acknowledged the difficulty in knowing an actual date but worked out a generalized plan that we finalized. I didn't have as much cash for a lavish wedding, but I felt annoyed at times when I was treated as if our wedding was not as important as the rest. The owner was very difficult dealing with at times, and at some point when it came time to sign the contract with a concrete date they went awol. For a good week I was frantic in trying to find potential new venues at short notice. Thankfully they did eventually get in touch and the venue looked just the way we wanted, but by the end of it we were all pretty upset. I'm aware of other couples that had the same experience.
3) We had the majority of his family flying in from overseas so that took planning between 15 people or so. The hardest part was booking a hotel which was apparently problematic because of the Pope (no idea but that was the excuse for the severely full hotels and high prices).
4) The day of we had one party member that really caused some problems. I ended up being shoved in a big closet at the last minute and my photographer and bridesmaid got me dressed to get me away from the situation. I hadn't a clue what I even looked like!
5) The stress was often severe. My husband took care of a lot of things on his side of the pond but there was only so much he could do. By the time he got here and was able to help more he really saw how much of a toll it had taken. There were a few times we wanted to just go elope because of the stress! And I should say there is no shame in that either. People often want the big celebration, but when you think of the money and time, I don't know if we would have done it again. We did get the special day we wanted, even if it wasn't 100% exactly as we had originally wanted.
My last piece of advice is everyone always makes a big deal about the dress, but pay attention to what is going on your feet. I had originally wanted combats a friend had painted which my family threw a fit about, and pushed me to get heels which then the bridal company lost. They offered backups. Well they were the absolute worst things - bloody blisters, dye that ran straight off... get what is comfortable for your feet the rest of the noise can shut up about it!
My point is a small or medium sized wedding is doable depending on several factors and how much help you have, even at short notice. But I certainly wouldn't recommend it. Most people do a courthouse ceremony.. I've been to one of those and it wasn't for us, but it absolutely works in a pinch.