Well, the paramedic had the closest answer, but still not completely correct.
"Clogging" of the aorta
takes years. The person eventually develops claudication (pain in the legs with walking due to not enough blood). However, by the time the aorta is completely closed off, the body often has created it's own bypasses (called 'collaterals).
We see maybe half a dozen of these a year. If the patient is otherwise healthy, we usually clean out the blockage and do what's called an aorto-bifemoral bypass. If they're not healthy, we do an axillo-bifemoral bypass. In this, blood is routed from the axillary artery
(in the armpit), down the side of the chest and into the legs.