Did the possible Chicxulub asteroid impact around 66 million years ago that made the dinosaurs and many other species extinct, cause the Earth to wobble? How large was the area, where they could "feel" the impact's consequences?
The whole Earth "rippled" after the Chicxulub impact. By ripple, I specifically mean surface displacement. Current models indicate that it rippled enough that most of the dinosaurs and other species with brains certainly would have felt the ripple.
How much did the Earth ripple? Well, that depends on the location. Meschede et al.  in their paper Antipodal focusing of seismic waves due to large meteorite impacts on Earth, visualize a computer model of the surface wave displacement due to the Chicxulub impact in the following figure:
Note that the displacement doesn't get much smaller than 1 centimeter, which is certainly large enough to feel over the order of tens of minutes. As another point of interest is that their model shows large displacement near the antipodal point, which some geoscientists correlate to the increased volcanic activity at that time in the Deccan Traps. Also note that these are just the seismic waves. We know from geological evidence at least from the Southeastern United States, that the resulting tsunami was much bigger.
As far as a "wobble", or change in angular momentum, the Chicxulub impact was too small to have a noticeable effect for the dinosaurs. JamesK has a nice example here: If an Asteroid was to strike the Earth, would it affect the Earth's rotation?.