gregzyme3 :
Rogue Leader :
Depending on the game it will be passable. It won't be an unplayable bottleneck at all. However in any title that is CPU heavy (think RTS games or anything multiplayer that the cpu has a lot to keep track of) you may notice some slowdowns.
Personally I would live with it until you can afford to do the upgrade right. Throwing as little money as possible at the cheapest thing that won't bottleneck it does not make good financial sense.
Would you think that the Intel Core i5-4590 3.3GHz Quad-Core Processor and the Asus H81M-K Micro ATX LGA1150 Motherboard be a poor idea? Or should I save further for a better cpu?
Its significantly better than what you have and a good combination. The problem is its a generation older hardware still.
However if I were you I would hold out a little and save up for an i5-6600k, a Z170 motherboard, and some DDR4 ram. Its faster, overclockable so in the future if you want to squeeze bit more out of it you can, and the next generation of Intel processors should work with it, so should you a couple years down the road want even more power there will be processor upgrades available to you.
When it comes to computers buying the newest fastest thing you can afford often pays off in dividends later in life.