There was construction going on last June when we there and it really didn't affect us at all. There are some construction vehicles there during the day, but there was always parking available.
We were there in June last year also. We didn't have any issues parking. Were able to get a spot near the walkway to the DVC pool every time we moved the car. Honestly, getting around by foot was more cumbersome with the construction at that time lol
We were just there in February and had no problems with parking. Convenient for us was that our room was directly across from the elevator that unloaded by the quiet pool/parking area. It was a quick and easy jaunt from the car to the room.