I believe you can have two nvidia quattro cards installed and each one can be split into two. I also think that one of them can handle four monitors but I am not sure about that.
As far as 'cheap' goes, that is another problem as i don't think that they are that cheap.
Well, you either want to get a motherboard that can handle 2 graphics cards and get 2 graphics cards. The cards have to be capable of driving 2 monitors each. My 2 X 7600GT's can although I have never tried it. Or you could try one of these USB video converter things...no clue how well they work though. http://www.usbgear.com/USB-Video-Card.html
If you're going for a one slot solution the Asus EAH 3870 X2 1GB is born with four DVI outputs allthough the $359.99 (newegg after mail in rebate) can't excactly be called cheap. matrox also have some cards that support four outputs, however they're all both more expensive and weaker than the card from Asus.
My (4) display stock trading station. I have solved the 4 monitors issues as follows:
Core i7-2600K Intel, Gigabyte motherboard GA-H67A-UD3H-B3, 16GB Ram DDR3-1333, 1TB WD Black 64 Cache HDD, Corsair 550Watt PSU, (1) Gigabyte Gv-N550OC-1Gi Video Card, (4) 24" Asus LCD/LED Displays. (2) DVI cables from the displays run to the graphics card. (1) DVI cable runs to the DVI plug on the motherboard, and (1) HDMI cable runs from the last display to the HDMI port on the motherboard. The built-in graphics drives (2) displays and the Video Card drives the other (2) displays. One thing left: Go to the Bios "Advanced Bios Option", in the menu go to "Init Display" and change (PCI-Default) to "Onboard". The on the menu "Onboard VGA" change "default-enable if no ext peg" to "Always Enable". Reboot, update software from manufacturers site. Go to Windows display setup via start button and assign and position each display in order and properly aligned. I have been doing this for 5 months without a problem. Good luck!