Hi,
If your two border routers already use BGP and talk BGP to each other - even if it's only for the default route - you could give router 1's route a higher preference. If router-1's link dies, everything goes through router-2.
You could even add your central switch as another BGP peer (peering with your border routers), which only gets default-route adverts from your border routers, with one router preferred over the other. In that case, if your border router dies (and not only the uplink), everything goes through your connected router.
I'm assuming that your two routers talk BGP to the providers and to each other.