Your router should be able to accept and transmit data pretty much as fast as
you can throw data at it, up to its maximum rated speed. I think it's highly
unlikely that your router is responsible for what you're experiencing, unless
it's dying on you, in which case I would expect it to just die rather than slow
traffic down.

It may be that you're just trying to access a very, very popular site and the
bandwidth problems are actually at the server end.

Verizon, however, are known to have traffic shaping measures in place,
particularly to limit p2p, but they may have extended it to other services or
high usage customers. I would strongly suspect that this is the culprit and
would strongly recommend switching to a better ISP.

We had that trouble awhile ago with our cable modem losing
connectivity. Web surfing became like we had dial-up. Our ISP replaced
it for us and no problems since then.
We had to call them and they tested the modem from their end.

I had a Linksys router that died a slow and painful death. First symptom was
that it stopped streaming Pandora.

My ISP had us set up for a high-speed burst on initial downloads that then
tapered off to a lower speed for long downloads. This really messed up the
buffering algorithms for Netflix. We had our ISP switch us to a constant-rate
download speed, and Netflix worked much better.