If House Republicans force immigration reform to conform to the "Hastert Rule" it could kill the legislation, Rep. Luis Gutierrez (D-Ill.) said Sunday.

House Speaker John Boehner (R-Ohio) has promised to only bring the bill up for a vote if a majority of the GOP caucus supports it. But Gutierrez told CNN's "Face the Nation" that a bill that gets a majority of Republicans will produce a "stalemate."

Appearing with House Judiciary Chairman Bob Goodlatte (R-Va.), Gutierrez said that only a bipartisan plan would work and that House Republicans' current path is "going to lead us to nothing."

If Boehner lets “a small group ... control the debate and the future on this issue ... we will then end in a stalemate and an impasse once again,” Gutierrez warned.

“The speaker of the House now has to decide whether or not he is going to allow the American people to speak,” he said. “There are a majority of Democrats and Republicans who are ready to solve this problem.”

Goodlatte countered that House Republicans are approaching the problem "methodically." The resulting legislation, he said, could end up getting large majorities of both Democrats and Republicans. But the chairman once again reiterated his opposition to a "special pathway to citizenship" for illegal immigrants.