Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Distraction; Workload; Situational Awareness
Conflict Airborne Conflict; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance
Human Factors; Airspace Structure
We were on the KORRY3 arrival but had not yet been cleared to descend via the KORRY3. I queried ATC as we were beginning to be high on the arrival. They cleared us to descend via the KORRY3 arrival and the First Officer (FO) selected 10;000 feet on the altitude preselect as the hard altitude and began a steep descent of over 2500 FPM to comply with the restriction at KORRY. ATC then changed the clearance to descend via the KORRY3 arrival except maintain 12;000 feet. The FO selected this new altitude and continued the steep descent anticipating clearance to 10;000 feet.At this time ATC began talking with a VFR aircraft that was in the arrival corridor at 11;500. The VFR aircraft agreed to turn off the track at ATC's suggestion. New York then re-cleared us to descend via the KORRY3 arrival so the FO set 10;000 feet again on the altitude pre-select. We were now showing a solid TCAS blue target for the VFR aircraft in question and shallowed the descent as it looked as though there was a possible conflict. We also began looking outside to see the aircraft but it was below a broken cloud deck. We then realized we would miss the hard altitude at KORRY and steepened the descent. We still missed the crossing restriction by one or two miles. ATC did not say anything.In retrospect; I should have told the FO to concentrate on flying the arrival (as we knew it was tight to make the KORRY crossing restriction) and I should have focused on possible aircraft conflict. Instead we both focused on the threat and neglected the arrival. If all else failed; we could have complied with a RA if it had happened.
[Report narrative contained no additional information.]
Air carrier flight crew reported that on descent to LGA on the KORRY3 arrival they slowed their descent due to VFR traffic and did not make the crossing restriction.