One of the main differences between the entry level saws and the more expensive ones is weight. Simply put, a heavier saw just vibrates less. My first saw was the Craftsman 16". I bolted it to a piece of 3/4" plywood, then clamped that to my workbench when I wanted to use the saw. Still vibrated, but much less than with the saw just sitting on the bench.
I upgraded from the Craftsman to the Porter Cable. This saw came with a stand. Big difference in handling. However, I wanted to cut down some of the vibration even more, so I laid two 70lb sandbags across the cross-members of the stand. Worked like a charm, significantly reducing the vibrations.
I now drive a Delta 40-690, with two sand bags on the cross-member. Almost no vibrations now.
The part that interests me about your situation, is that you were able to cut before without too much trouble. Are you sure you had the blade installed correctly, AND properly tensioned. A saw will vibrate like crazy if you haven't tensioned the blade. Trust me on that one!