Have you tried a few basics such a different cord and/or a different USB port? If so, you might want to try restarting the Mac in Safe Mode by holding down the Shift Key during startup (until you get to login screen). This can take several minutes. You can also try creating a new User Account (this can be deleted later if you want) and try connecting to the new account.
Have you done a hard boot of the iPhone? Press Up volume>Press Down Volume>Press and Hold Power Button until you see the Apple Logo, then release (this may take up to 45 seconds or so).