Is it possible to Idle, and get trading cards?

Solution 1:

Yes.

Steam Trading cards are given out based on time spent in-game. Steam doesn't have, for most games, any way to know whether or not you're actually doing anything, just whether you have the game running or not.

Solution 2:

Yes,

It is also interesting to note that you can run many games at the same time to get the trading cards, and you can even get them from game launchers if you want to conserve computer power.

Solution 3:

Yes. You almost don't even have to idle. I got mine pretty much just for starting up portal 2. It's pretty much the same system they have for item drops in TF2