Yes, the dict will be stored in the process memory. So if it gets large enough that there's not enough room in the system RAM, then you can expect to see massive slowdown as the system starts swapping memory to and from disk.
Others have said that a few million items shouldn't pose a problem; I'm not so sure. The dict overhead itself (before counting the memory taken by the keys and values) is significant. For Python 2.6 or later, sys.getsizeof gives some useful information about how much RAM various Python structures take up. Some quick results, from Python 2.6 on a 64-bit OS X machine:
>>> from sys import getsizeof
>>> getsizeof(dict((n, 0) for n in range(5462)))/5462.
144.03368729403149
>>> getsizeof(dict((n, 0) for n in range(5461)))/5461.
36.053470060428495
So the dict overhead varies between 36 bytes per item and 144 bytes per item on this machine (the exact value depending on how full the dictionary's internal hash table is; here 5461 = 2**14//3 is one of the thresholds where the internal hash table is enlarged). And that's before adding the overhead for the dict items themselves; if they're all short strings (6 characters or less, say) then that still adds another >= 80 bytes per item (possibly less if many different keys share the same value).
So it wouldn't take that many million dict items to exhaust RAM on a typical machine.