In extreme cases (like one of those 22ga super cheap PSU cables) the cable wires can get hot (P=I^2R). If bundled up tight that heat just builds until something melts and then shorts out. Kind of a nightmare scenario, thankfully not something that happens too often based on the lack of any posts I've ever seen where it's happened.
Usually happens when ppl use adapters, especially Sata to 6+2 pin or molex to 2x 6pin etc.
P=I²R is only part of it. The gpu demands a certain amount of power to function, so that's a constant. Both sides of the = must remain the same, so as resistance builds, amperage drops at the receiving end, so amperage draw is increased at the source to compensate for the loss. As the amperage goes up, heat goes up, which increases resistance, then amperage, rinse and repeat in an ever climbing cycle until the resistance and amperage is great enough to create enough heat to melt the weak point, and you get a fire in the pc.
VRM's and gpu are no different than VRM's and cpu, there's going to be voltage fluctuations because of loads, but that's all board related, any voltage concerns as supplied by the psu are no different either, voltage isn't affected by guage when talking about wires a foot long. Even 22ga supply wires. The longer the wire, and smaller the guage, the higher the resistance.
A 10ft length of 18ga has a 1.06% voltage drop at 12vDC, or basically 0.128v. Most psu supply are 12-18", so figure a voltage drop of @ 0.013v, 12v being 11.987v ± at the gpu. That's moot, especially considering there really aren't any 12.0v outputs as a constant value, most psus range from @ 11.8v to 12.1v, 12v really is more a designation than actual output.