Hyperkalemia (too much blood K+) caused by kidney failure is because the kidney is not clearing excess K+, and most K+ excretion is by the kidneys. Usually kidney failure alone isn't sufficient to cause hyperkalemia (Lehnhardt and Kemper,
2011), and note that kidney failure can cause problems via many other mechanisms besides hyperkalemia.
The reason that hyperkalemia causes problems with heart and other muscle function isn't directly because of the Na+/K+ pump, but because of how the electrical potential of cells controls contraction. Cardiac myocytes, like most cells, have a negative resting potential, with high K+ inside and low Na+ and Ca2+ inside, and a resting conductance that is higher for K+ than the other ions. When the cell is depolarized to around -40mV, a rush of Na+ and Ca2+ comes in that further depolarizes the cell and also causes the muscle contraction.
Normally, this "action potential" is terminated by opening K+-channels, which returns the cell to a hyperpolarized/resting state by letting K+ ions flow out, ready to fire another action potential and contract again. However, the resting potential is determined by the Goldman equation and depends on the concentration of each ion both inside and outside the cell. The reversal potential for K+ depends on there being a lot of K+ inside the cell, and very little K+ outside the cell. Therefore, it takes a large negative potential to keep K+ in equilibrium. As the K+ concentration outside the cells increases, the equilibrium potential for K+ gets closer to 0 mV. Eventually, cells can't repolarize after contraction and effectively stay in "contraction mode" without relaxing.
Although the Na+/K+ pump is somewhat dependent on the concentrations of Na+/K+, the typical role for that pump is to push K+ ions into cells and pull Na+ ions out. If blood K+ is high, that will not do anything to prevent the Na+/K+ pump from operating, so suppression of that pump is not having any mediating role in this process.
As a side note, KCl is used in lethal injection in the United States as the final drug administered, which stops the heart by causing immediate hyperkalemia.