This kind of thing apparently happens occasionally. There was a heavy meteorite shower at the Cambrian/Ordovician border about 480 million years ago (see here for example):http://www.sciencemag.org/cgi/content/abstract/278/5335/88
This hasn't been linked to any very large impact (though there are some candidates), but then most would have been subducted or eroded away by now. However the flux of small meteorites was so heavy that quarry workers at Kinnekulle in Sweden who happen to work in just the right limestone layer regularly find meteorites (L-chondrites).
This impact shower has been linked to the Cambrian/Ordovician extinction but there is no conclusdive proof.
There was also a shower of impacts in the late Eocene c. 35 million years ago. There are several craters of approximately this age (Chesapeake and Popigai are probably the most famous ones). This has usually been explained by a comet shower caused by some upset out in the Oort cloud, but there is no conclusive evidence for this.
There was a minor extinction episode near this time ("le Grande Coupure"). but there is good evidence that this was due to the Earth shifting from "hothouse" to "icehouse" climate, and that this in turn was caused by tectonic changes (the opening of the Tasman Sea and the Drake Passage which isolated Antarctica climatically).