The chief goal in Mario games has always been survival. You're expected to traverse the level, defeating as many enemies as possible along the way, so that you reach the end without death. Coin collection, along with discovery of secrets and acquisition of points, have always been secondary goals. Now, coin collecting is front and center (well, still behind not dying) and those background elements are among the most important.
NSMB2 increases the importance of coins by keeping a running count through your whole game. It also makes sure money is on your mind by putting coins absolutely everywhere. They curve around moving platforms like in New Super Mario Bros. Wii (highlighting some engine improvements over the DS game), they fill up secret areas inside special gold pipes, and they just generally make up an overwhelming presence in the stages.
There's even a new powerup that's all about coins: a gold Fire Flower that causes everything in its explosive path (enemies, blocks) to turn into coins. The other powerup new to NSMB is the raccoon tail, which works just like in Super Mario Bros. 3. You know that one already. Coins were previously just a thinly veiled signpost to show you the path through a level, but now they're the central element of the level.
Having only played a single level, I don't know how pervasive or interesting the greed motif will be in the full game. I just love that it's possible to tweak a single element of a very familiar series to make something new. I also love coins, so it's a promising game.