Cole, a deputy majority whip, told The New York Times one-third of Republicans typically want a bill to pass and support it, while another third vote against bills they oppose.
That leaves what the Times called the "Vote No/Hope Yes Caucus."
House Republicans are currently in Williamsburg, Va., for their annual conference, which includes developing a strategy for working with, or against, President Barack Obama and the Democratic majority in the Senate.
Cole told the Times about a conversation with a member of the Republican caucus about legislation aimed at avoiding the tax hikes and budget cuts known as the fiscal cliff. He said he did not want the bill amended because it might die in the Senate -- exposing Republicans to blame for a catastrophe.
Cole voted for the bill.
"So I said, 'What you're really telling me is that you want it to pass, but you don't want to vote for it,'" Cole said.