In a Presidential election, roughly 60% of the voters actually cast ballots.
In the primary elections preceding the general, roughly 30% of the voters cast ballots, and that's in a good year.
Since that's for two parties, the candidates for each party are chosen by about 15% of the voters.
The most liberal 15% of the electorate - those for whom the current situation doesn't really work well, at all - are largely among that 40% that doesn't vote, even in the general.
The most conservative 15% of the electorate, though, votes. And since most districts and even states are "safe" for one party or the other, the typical GOP member of Congress is chosen by the most conservative 15% of the voters in a conservative district or state.
And that's why polls showing that 90% of voters favor background checks, or 80% favor a higher minimum wage, or anything else you care to name, simply don't matter. The Republicans in Congress answer to the most conservative 15% of the national electorate, and you would need to poll those voters to determine what motivate Boehner and McConnell.
And I think if you did poll them, you'd be terrified.