The dog caught the car, but it has no idea how to steer the wheel ...

"Their policies could actually increase immigration. And they have no idea how to control the fear they rode to victory."
"I’ve often wondered what it would be like if, here in the US, a border hawk Republican like former Arizona Gov. Jan Brewer or Ted Cruz or Donald Trump were actually elected president (or even appointed head of the Department of Homeland Security). Having persuaded their followers that the US/Mexico border was lawless, they’d suddenly have to persuade them it had been made safe. Otherwise, they’d be yet more failed politicians who couldn’t keep their promises and America safe."
Pro-Brexit politicians are the dog that caught the car. Now immigration is their problem

The dog caught the car, but it has no idea how to steer the wheel, not to speak of where to go. Is this the writer of this article intends to say?
I wonder what would happen if the dog instead caught a horse-drawn carriage that is not as fast as the car? Would it want to draw the carriage? Or, would it want to sit on the box?