The charts above can offer a clue as to why. They were made with information from a 2013 Kaiser Family Foundation survey. Note that 61% of the American public thinks this country spends too much on foreign aid. They think that because they don't have a clue just how much of the budget goes to foreign aid. The average answer from Americans is that 28% of the budget is spent on foreign aid, and answer range from 1% to 51% or more. But 96% of the public is wrong. Only 4% know that foreign aid is only about 1% of the budget (or less).
Cutting foreign aid to balance the budget is the one area most Americans would agree on. But we could completely eliminate foreign aid from the budget, and it wouldn't make the deficit any smaller -- and it certainly wouldn't even come close to balancing the budget. The sad truth is that this is not the only area of the budget that people don't understand. And that is what leaves them vulnerable to believing the lies being told by the Republicans.
I would say that people need to educate themselves about budget matters, but that's not going to happen. The best we can do is try to expose those lies as they are told, and hope that enough people see the truth and stop electing the liars.