Yes. Connect a third device to both routers, configured to route traffic in the manner you prefer (load balancing, round robin or such that computerA uses routerA and computerB uses routerB).
There are a large number of options depending on what scale of solution you're looking at (eg, is this a 2 person solution for a pair of 2 Mb/s DSL lines, or a 200 person solution for a pair of 50 Mb/s DSL lines).
Sounds like you're after a policy based routing or similar, though there's a non-trivial challenge in differentiating between web browsing and downloading over HTTP. I know that pfSense has multi-WAN capability and it may do what you're after.