My MakerBot 2 jams after a couple hours of prints
As you stated, it could be a result of the material beginning to melt before the extruder. Here's a few things to look out for:


Is your extruder temperature appropriate for the material? Typical printing temperatures can range anywhere from 200 - 225&nbsp;&deg;C for PLA (depending on the supplier). Often, if the extruder is too hot, the material will bubble or over extrude.
Is the material of proper quality? There's a reason MakerBot Industries wants you to use their filament (besides putting their hands in your pocket book), and that is repeatability. They've tested their filament on their hardware and ensured that the material will extrude with regular print settings.
Is the material being stored properly? Sometimes people forget to store PLA in a dry place to avoid absorbing moisture in the filament. If moisture is absorbed, it can perform poorly in the print. Indications of moisture can include a slight steam from the extruder and/or bubbles in the extruded material (similar to overheating).
Are the fans operating correctly? If the fans aren't running or aren't running enough, the filament begins to heat further up the extrusion assembly (closer to the drive gear) which can inhibit extrusion. I know that MakerWare/MakerBot Desktop has been updated lately with more emphasis on controlling fans for active cooling, so make sure that your fan(s) are operating for duration of the print as necessary.


All and all, your filament is getting too hot. If you can't determine the sudden change, consider printing with a lower extruder temperature from now on. However, if you're using MakerBot filament (or similar quality) then I would definitely verify that your machine is calibrated, wires are fully connected, and settings are double checked. If all is as expected, then you should call MakerBot support (since they're closed source now, they technically have an obligation to help you) especially since the machine is so new.