The fat cells play a fascinating role in attempting to compensate for glucose uptake deficiencies. Fat cells are now considered by experts to be an essential part of the endocrine system, in that they can orchestrate energy management by many organs of the body by releasing hormones into the blood . Fat cells are able to absorb excess sugar from the blood and convert it into fat. The fat will later be released into the blood stream as fatty acids and triglycerides, which offer an alternative energy source to the muscle cells (and most other cells of the body) - an alternative that does not suffer from the problem of membrane transport, which is specific to glucose.
In a situation where glucose transport is defective, the fat cells appear to: (1) program the muscle cells to consume fats rather than sugars, and (2) take upon themselves the task of converting as much of the incoming sugar as possible to stored fats. The fat cells accumulate fat whenever the blood sugar levels are high, and then release it into the blood stream whenever blood sugar levels are low enough. Thus they strive to maintain in the blood stream a steady supply of an alternative and more efficient source of fuel (fats) for the muscles to consume instead of sugar.
Through signaling involving a peptide released into the blood stream by fat cells, called leptin, fat cells are able to redirect the muscle cells to obtain most of their energy needs from fats instead of from glucose. However, as a consequence, the fat cells then become burdened with the task of of converting as much as possible of the incoming glucose to fats.
The fat cells must thus buffer up a reserve store of fats, and release fats into the blood to provide nutrition for the muscle cells during fasting conditions, when glucose is not available. After meals, when glucose levels are high, the fat cells are preoccupied with extracting glucose from the blood, and therefore are unable to release fats. Thus, they must provide additional triglycerides in advance of a meal, so that the muscle cells will continue to have food while the glucose is being taken up by the fat cells and converted to a renewed supply of fat. This safety buffer of triglycerides is what is responsible for the observed high fasting triglyceride levels of the obese.
If more dietary fats were consumed, fat from food sources would be available to the muscles while the fat cells are distracted with taking up glucose, and there would be correspondingly less glucose to convert. But because so much fat is needed to feed the muscles, and because so much excess sugar is going to waste, the fat cells find themselves unable to meet the demand, so they end up proliferating -- and the person becomes obese.
The fat cells also suffer from an impairment of glucose transport, as they rely on the same mechanism involving GLUT4 and insulin to transport sugar across their cell walls (Details) . Fat cells however are able to internally hoard both vitamin D  and calcium , so that they can improve somewhat their own abilities to transport glucose across their cell membrane. But this also leaves the muscles more vulnerable to glucose uptake inefficiencies, because it further depletes the availability of calcium and vitamin D in the blood. As long as the muscle cells use up fats as their energy source instead of glucose, and as long as the fat cells can maintain a good supply of fats in the blood, all will be well. This is the scheme that the fat cells are trying to perpetuate.