I signed on at 6:15 AM this morning May 4 to make park reservations for Saturday July 3. The first several times I just got the annoying Stitch "Someone Ate The Page" screen. Then I tried signing in through the
Disneyland app on my cell phone. It took me to the same "disneyland.disney.go.com" portal, where I had to sign in again, but this time everything worked! So I can confirm that the reservation page was active, and had already opened up for July 3, by at least 6:15 AM.
My wife and I have Park Hopper tickets, and both California Adventure and Disneyland were available as the first park to visit, or the "all day" option. I chose California Adventure, to get in early to see Avenger's Campus. We'll be able to go to Disneyland that day after 1 PM.