If you're happy with the HDMI port driving your 4K monitor (which means you're running at 30Hz), it seems that a GTX 660 or better will work. (AMD cards have similar port layouts)
DP: 4K @ 60Hz
HDMI: 4K @ 30Hz
2xDVI: use dual-link DVI->HDMI adapters (which are expensive, granted)
If your monitor supports being driven by 2 HDMI cables, you can use 2 of the HDMI ports to drive one of the monitors at 60Hz.
I am presently happy with 30 Hz—very happy in fact because the resolution is so spectacular. However, if I owned three of these Dell monitors, I would definitely want them to all function at 60 Hz. And I don't believe the dual-link DVI ports on the nVidia cards will do greater than 2560x1600.
I think the only way to drive three of these Dells at 60 Hz would be a 3x DisplayPort GPU. nVidia and AMD, are you listening? With an affinity for a wide spectrum of GPU options, especially at nVidia, why is this not a thing?
It's probably worth testing if you can borrow a dual-link DVI->HDMI adapter, but I would be surprised if it didn't work. Those adapters don't actually do a full conversion; they work by telling the video card to send HDMI signals out of the DVI pins. It's obviously physically possible, 4K@30Hz requires less bandwidth than 2560x1600 @60Hz.
nVidia is supposed to release its next generation of cards (AKA Maxwell) in the spring. They will likely support HDMI 2.0, which will support 4K@60hz. I'm really surprised that the new AMD cards that came out this fall don't support HDMI 2.0.
DP: 4K @ 60Hz
HDMI: 4K @ 30Hz
2xDVI: use dual-link DVI->HDMI adapters (which are expensive, granted)
If your monitor supports being driven by 2 HDMI cables, you can use 2 of the HDMI ports to drive one of the monitors at 60Hz.
Of course, I haven't actually tried this.