I noticed in your sample, you were using leaflet-0.7.5 and used layers: MQ.mapLayer(), as a basemap.
We are developing with the newer v1.0.0-beta2 version of leaflet.
When I tried to use this layer it screams "TypeError: this._adjustTilePoint is not a function
https://www.mapquestapi.com/sdk/leaflet/v2.s/mq-map.js?......Line 61 in firebug.
I am however able to use the standard Leaflet basemaps and see the traffic for my prototype.However I have to admit, I like your basemap better.Any idea of when you will be supporting the newer leaflet api?