This test fails because it will never pass the Auth::attempt() function call. I put a dd() statement to prove that it won't make it. 
If I remove the two Auth::shouldReceive() the code will run the first dd() statement.
If I keep even one Auth::shouldReceive() the first dd() statement will never get called.
If I add ->twice() instead of ->once() there are no errors thrown which is odd because it should complain that it has only been called once.
If I place a dd() statement at the first line of the controller it does not run until I remove the Auth::shouldReceive() functions.
I must be something silly that I'm not getting because I've looked over many tutorials.
Controller
public function postLogin() {
    $email = Input::get('email');
    $password = Input::get('password');
    dd('Does not make it to this line with auth::shouldReceive() in the test');
    if (Auth::attempt(array('email'=>$email, 'password'=>$password))) {
        dd("Doesn't make it here either with auth::shouldReceive() mock.");
        $user = Auth::user();
        Session::put('user_timezone', $user->user_timezone);
        return Redirect::to('user/dashboard')->with('message', 'You are now logged in!');
    } else {
        return Redirect::to('user/login')->with('message', 'Your username/password combination was incorrect')->withInput();
    }
}
Test
public function testUserTimezoneSessionVariableIsSetAfterLogin()
{
    $user = new User();
    $user->user_timezone = 'America/New_York';
    $user->email = '[email protected]';
    $user->password = 'test';
    $formData = [
        'email' => '[email protected]',
        'password' => '123',
    ];
    \Auth::shouldReceive('attempt')->once()->with($formData)->andReturn(true);
    \Auth::shouldReceive('user')->once()->andReturn($user);
    $response = $this->call('POST', '/user/login', $formData);
    $this->assertResponseStatus($response->getStatusCode());
    $this->assertSessionHas('user_timezone');
}
 
                        
The problem was that I had
parent::construct()in the constructor of my UserController. Apparently this causes issues with mocks.I assumed this was necessary to have
parent::construct()because I had a custom constructor in UserController.