A House Democrat seeking to forge an immigration deal warned Sunday that Speaker John BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery 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 Vicente GutierrezWe are running out of time to protect Dreamers Gutiérrez makes moves toward presidential run: report Gutiérrez leaving Congress, rules out bid for mayor, governor 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 Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery 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 GoodlatteRobert (Bob) William GoodlatteRosenstein to testify before House Judiciary Committee next week Conservative pressure on Sessions grows Clock ticking down on NSA surveillance powers 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.