High-end cards definitely are not needed to play the game. Hell, I sometimes play on a MacBook Pro with an Intel GPU and it does just fine with high quality settings at the "low" resolution of 720p. Now, if I try to use that machine to drive a high resolution display, well, it's not going to do so well at any part count.
My takeaway from Renegrade's and eddiew's comments are that the limiting factor in KSP is often the CPU, and a better CPU (in terms of raw single-threaded performance) is essential to getting decent performance with high part count vehicles.
But that's not particularly useful. Let me explain why. Here's what I'm imagining:
If you take some variable like Part Count which impacts the game's "CPU boundedness" and some other variable like Resolution which impacts the game's "GPU boundedness," put them on two different sides of a plot then you can draw something like a performance gradient. Imagine it's measured in FPS or something, the specifics don't matter right now. On this gradient, you can trace the curve where FPS=60. This describes the capabilities of a particular piece of hardware running Kerbal Space Program.
Because this curve looks different for different pieces of hardware, you can extend the gradient into additional dimensions describing that hardware. If it were possible to boil all hardware configurations down to a single value like "Dollars" then you could imagine it in three dimensions. Or, you could do something similar by limiting yourself to varying only the CPU, or varying only the GPU, and so on. Doing so, FPS=60 becomes a surface describing what hardware to buy to achieve a particular performance target. And I'm wondering what that surface looks like.
Looking at it from a different angle, you could say to yourself that any number of parts greater than X is unreasonable and beyond that all bets are off. Take the slice where Part Count=X and look at the FPS=60 curve for Dollars and Resolution. Pick a resolution you think is good enough and find where the FPS=60 curve crosses that line. This is how much money you need to spend to hit that target.