I also imagine raccoons and possums. Maybe even sloths.
When I say rodent-like, I imagine that small creature that was hiding in a hole while the T-Rex was out and about. Also I have a habit of picturing a raccoon in my head when I hear the word "rodent". According to what I know, the extinction of the dinosaurs (if you believe in the evolution theory or if the evolutionary history happened this way) is said to have created an evolutionary opening to allow for mammals to get much larger, and a while afterwards, they became much larger than the ones we see these days. Now they say that mammals aren't doing very well, probably from rising temperatures.