It's true that each state gets two senators, but the rest feels like a misinterpretation. The Electoral College is separate from the Senate, where each seat is up for grabs separately, in elections that run for a third of the senate every two years (so that each Senator serves a six-year term). The other key point is that the Senate and the Presidency are regarded as separate offices, so that it *is* possible for different parties to control different branches, but this is by design. The US system was meant to more or less force compromise, between the States, the people, the Federal Government, and the parties that may or may not end up entering politics.
Whether it's succeeded is another matter, but the potential for different parties to hold different parts of the system is an intentional feature rather than a "bug".