Meat and veggies are just fine and quite healthy if done right. But they aren't magic. There are alot of people who eat paleo and drop alot of fat and then stall, because calories. You can't ever escape the math no matter what you eat.
Here are a couple warnings from my n=1 experience.
If you've never cut out grains and carbs before then meat and veggies diet will give you intestinal troubles. Like constipation... big time. There's plenty of ways to up the fiber and water intake. Eventually your body will adjust.
In the first two weeks you will drop an insane amount of body weight when you first drop carbs. Like 5-15lbs. This is 90% water. Glycogen in your muscle cells holds alot of water. This will mess with your head and make you think you're getting magic results. When you do refeed carbs you can easily gain 5 lbs after a couple meals. This will make you feel panic. Remember it's water, just head games.
If you go under 50grams of carbs per day you will eventually enter ketosis. Sometime between day 4 and 10 your body will hit the "low carb flu" as your body adapts to using ketones and fatty acids for fuel. You will feel like garbage. Confused, light headed and annoyed for a few days it will pass.
Also carbs aren't the enemy all the time. I wouldn't recommend lifting on no carbs ever. Refeeds help. Look into the Anabolic Diet by Dr. DiPasquale. There's a huge thread about it on T-NATION.