A 2 km diameter asteroid would make a huge impact. If it hit land, it would immediately & completely destroy an area the size of a large state (e.g., California) or a small country (e.g., France) by the force of the impact and widespread fire. It would leave a 30 km crater.
An ocean impact would generate global-scale tsunamis.
Hitting either land or ocean would kick up enough dust into the atmosphere to change the global climate. Crops would fail worldwide. The ozone layer would likely be destroyed. Lots of plant and animal extinctions would occur, but probably not a "mass extinction".
source: Report of the Task Force on Potentially Hazardous Near Earth Objects, U.K., Sept 2000
IIRC, the one that killed the dinosaurs was 10 km (global devastation).