no, you can book one, just be realistic on a few things.
If you want to stay on property, then as long as you are booking at least 60 days out, you should be fine. Rooms should be available in all categories, and there are discounts gonig on. I posted them about a week or so ago, let me look.
the 60 day mark i mention is that's when you can begin booking your FastPasses. FPs are ride reservation that get you through a special line at a selected time of day for each specific attraction you hold a FP for. Everyone gets 3 per day and once they are used, you can get a 4th, then 5th, etc. Rides do 'sell out' of FPs that's why the 60-day window is important. On-site guests get to select there on 60 days out, whereas locals and of -site guests cab claim them at 30 days out. I guess late June is inside of 60 days but till not 30 so you still have a shot at decent availability. Google Disney's FastPass for a full explanation of how it works.
If you are looking to stay off site, then book it before 30 days or else you will kinda screw yourself with FPs.
It is possible to do the parks with no, or average FP experiences, just accept that you'll be spending more time in line on the major attractions.
As for dining, people can start booking their dining 180 days away, i know its a while. So popular restaurants do fill up and it is hard to get a table. But there are a bunch of restaurants on property and people hoard and then cancel reservations all the time, so it helps to keep checking. You can move or cancel reservations up to 24 hours before. Also, there is really good dining at Disney Springs—which is kind of like a bar and shopping district at WDW—really good ones. And most of them are not owned by Disney. So what that means is that they have some of their tables set aside for the WDW reservation system, and another set that they keep open for locals and sites like Open Table. So if you cant get a reservation through WDW's site, try calling the location directly or check open table.
But sit down dining is not the only place to eat a meal...there are lots of good counter service locations (walk up dining) within the parks and they will not take an hour+ of your park time. Its all in how you want to experience the parks.