Hi Ctrm,Welcome to the Healing Well 
Wrapped Club! While I wouldn't tell you that you should deviate from your surgeon's recommendations, but I can tell you that eating protocols vary widely between surgeons.
While some start people on liquids for a week or so, then allow them to progress to soft foods, others have a much more liberal eating recommendations. First, keep in mind that your wrap will become increasingly more swollen in the first two weeks, with peak swelling occuring on or about the 14 day mark. During that time your swallowing will become more difficult. Once peak swelling occurs, you'll be on the other side and that swelling will gradually decrease, allowing you easier swallowing.
My surgeon was one of the liberal ones, and I can tell you that it all worked out just fine for me. The most important thing is to always listen to your body and follow its lead. If you can surrender to your recovery and follow it where it takes you, you'll find your recovery much easier. It is as it is. Go with the flow, and let things come to you in their own time.
While during the first two weeks there were times when I didn't even WANT to swallow due to discomfort (of course, I did swallow), I was never limited to liquids, except for my one-day stay at the hospital. I went home on soft foods, and my surgeon put me on "anything that could be chewed to a liquid" after my follow-up on Day 5 or 6. He did warn me against steak and untoasted bread for about 8 weeks. He trusted me to use my judgement with foods, and I can tell you that I didn't have any trouble with this. My mouth was my blender, and I took small bites and chew, chew, chewed things thoroughly until they were a smooth, creamy consistency. If I couldn't chew whatever it was to a liquid, I'd deposit it discreetly in a handy paper napkin.
Joy is right in saying that cold things an create discomfort by creating esophageal spasms. Stay away from iced and carbonated beverages, and avoid straws, as they create more air in your stomach, adding to the bloating issues. You mentioned hamburger...from my experience, it's one of the tougher things to get through the wrap...it always maintains a consistency that's tougher to swallow during the early healing stages. Chicken works much better.
Here is my early recovery journal:
https://www.healingwell.com/community/default.aspx?f=45&m=2183443
Also here are a couple of eating protocols. They will provide you with some guidance as you make eating choices:
http://www.upmc.com/patients-visitors/education/nutrition/Pages/diet-after-nissen-fundoplication-surgery.aspx
http://www.nissenfundoplication.com/nissen-fundoplication-diet
Again, glad you've joined us!
Happy healing!
Denise