It's not just that the people feel betrayed. Through the rhetoric of the Right Wing Media (Limbaugh, Ingraham, Fox News, various politicians, etc.), they have been convinced that what liberals and Democrats have done is absolutely evil, and that voting for Republicans will stop and reverse this. It is not a matter of compromise or improvement; it is a matter of defending what is good and righteous, with the fate of the Nation in the balance.
This message has been very successful for the Republicans for the past couple of decades. It has energized its base and allowed them to achieve significant victories in getting candidates elected to Congress.
But it has come at a price, that being that it requires a complete victory. You can't have a partial victory when the fate of the Nation hangs in the balance. You either win or die, swim or sink, defeat the evil Democrats or be defeated. And, so far, the evil Democrats haven't been defeated. They are holding their own.
So what do you do when the stakes are so high? Who do you turn to when you're losing the war?
A strong leader. One who can take on the evil Democrats. One who isn't afraid of them, can bully them into submission, can get the policies pushed through by trampling over the opposition.
Or as one Trump supporter said on NPR this morning, a guy who "isn't a pansy" like all those in Washington.

When you hear, day-in and day-out, how we are at war with those who are destroying our country, and we are losing that war, then desperate measures are called for. Measures that might include ignoring the Supreme Court, ignoring Congress, ignoring those in the Military that what you want to do is illegal, ignoring reality if necessary (by saying that Mexico will build us a wall to keep their people out of our country

), and just getting the job done.
Trump supporters aren't evil or stupid. They've been convinced, through the relentless propaganda of the Right, that we are in desperate times and that things aren't changing their way. So they are willing to take desperate measures, because the stakes are so high. And the one who seems the strongest right now is Trump.
Thus we get a Republican front-runner who most of the Republicans can't stand. A person who is a liar and a bully. A person who promises the moon, but has no real plan or experience on how to get there.
But, really, how different is he from all the demagogues that have been preaching to the Right for years?