This ought to be easy, according to these new Pew numbers:
Gun control supporters can point to broad and consistent public support for expanded background checks. Fully 81% favor making private gun sales and sales at gun shows subject to background checks, little changed since January (85%). The proposal draws nearly equal levels of support from Democrats (83%), Republicans (81%) and independents (80%).
However, there's a however:
However, the Senate bill on background checks is far more divisive. Republicans are decidedly less supportive of this legislation than of the general idea of making private gun sales subject to background checks; 57% support the Senate bill, while 81% favor expanding background checks. Many of those who have reservations about the bill express concerns that it includes other restrictions beyond background checks, or that it opens a “slippery slope” toward more government power.
It's quite a testament to the extraordinary lobbying power of the NRA that even with 57% support from Republicans, a bill can't pass.