Listening to the tapes, UA2098 told departure that they had a 'hydraulic issue', they were declaring an emergency and the new destination was EWR. No mention of a possible tire burst on takeoff, you would think that LGA would want to check for FOD on the runway perhaps? Do UA A319's have brake temps or tire pressure indications? On widebodies these usually give you an indication of a blown tire in my experience.
25,000 pounds of fuel, 133 POB's, they were given immediate vectors for the ILS 22L but needed more time to 'troubleshoot' so they took vectors for another try. Tower asked if they anticipated any difficulty exiting the runway, UA2098 said no but they wanted the trucks standing by just in case. After UA2098 went off the side of the runway, the airport was closed, all aircraft hold position and monitor the radio.