A House Democrat seeking to forge an immigration deal warned Sunday that Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE’s (R-Ohio) pledge to only move a bill that a majority of his conference supports could create a “stalemate.”

The Speaker of the House now has to decide whether or not he is going to allow the American people to speak,” said Rep. Luis GutierrezLuis GutierrezDHS hires incense immigration supporters The Democratic Party playbook must change if liberals are to win the future Army vet slated for deportation over drug charges MORE (D-Ill.) on CNN’s “State of the Union” on Sunday.

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“There are a majority of Democrats and Republicans that are ready to solve this problem,” he said. “Will he allow a small group – maybe even a majority of his caucus – to control the debate and the future on this issue? If he decides to do that, we will then end in a stalemate and an impasse once again,” he said.

Gutierrez is part of a bipartisan House group seeking to craft an immigration bill

The Senate passed a wide-ranging bill last week with 14 Republicans joining Democrats to advance a measure which includes a pathway to citizenship for undocumented immigrants and tougher border security.

BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE has said the House will only move an immigration plan that a majority of the chamber’s Republicans back.

House Judiciary Committee Chairman Bob GoodlatteBob GoodlatteLawmakers reintroduce online sales tax bills Senators push 'cost-effective' reg reform Rob Thomas: Anti-Trump celebs have become 'white noise' MORE (R-Va.), speaking on the same show, said he did not think immigration reform would die in the House, and defended the “step by step” approach House Republicans are taking.

“I think the Speaker wants to solve this problem, he wants to do it methodically, where we examine each of these issues separately, and we are doing that, then he wants to find something that can pass the House,” he said, arguing that ideally a measure can be crafted that wins majorities in both parties.

Goodlatte criticized the Senate-passed bill, arguing it errs by giving undocumented residents legal status before it solves border security and other problems.