Strictly speaking the 8MB is the frame buffer size, not the video memory size, that will dynamically allocated upto 224MB (although any memory the video card uses will be stolen from the rest of the system)
Assuming you want to run 32bit graphics (the highest colour setting) 8MB frame buffer isn't really enough
1920,1080 * 32 * 8 / 1024 / comes to 8100KB which is 7.9MB or in other words.... pushing it.
If you try dropping the colour depth to 24bit you'd get 1920,1080 * 24 * 8 / 1024 / which is 6075KB (about 6MB) which will give you a far better chance of running in 1920*1080 resolution.
The 2048*1536 ABE mentioned above would only be possible in a colour depth of 16bit.
Ideally, a better graphics card would be the answer, they can be got pretty cheaply, but before anyone can recommend one we'd need to know which case you've got as that dell comes in 3 case sizes and which card to go for is going to depend in what will fit in your case.