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House Republicans leaders warned Wednesday against enactment of an "Obamacare-like" immigration bill and said they will ignore the Senate-passed bill, instead creating one of their own.

In a statement, after a closed-door meeting of GOP rank and file, the leaders rejected the bipartisan Senate bill that includes a path to citizenship and increased border security. They called that legislation flawed, The Associated Press reported.

Speaker John Boehner and other leaders said the House would take a step-by-step approach to rewriting the nation's immigration laws.

Meanwhile, House Minority Leader Nancy Pelosi and border-area Democrats tried to encourage their Republican colleagues to consider the Senate proposal. Last month the Senate passed its version of comprehensive immigration reform.

The legislation already includes input from both Democrats and Republicans, Pelosi said.

“Just about every element you can name is something that already has bipartisan support or has been initiated by the Republicans. I think there is a path to comprehensive immigration reform," she said.

She and four other Democrats on Wednesday argued the proposals should focus more on economics and less on border security.

“The Border Caucus feels very strongly, and it’s reiterated by the leader, about a pathway to citizenship, but we also feel very strongly that part of the security of our border has to do with economic security of our borders, has to do with ports of entry that are functional, enhanced trade and commerce, and has to do with full staffing of Customs," said U.S. Rep. Raúl Grijalva, D-Ariz.

Grijalva, who represents one of two districts in Arizona that border Mexico, told Arizona Public Media that a discussion about security that focuses on increasing fencing along the border is not enough. He cited the more than 5,000 migrants who have died in the desert or other border areas after crossing the international boundary.

“We’re asking that part of the consideration needs to be humanitarian support," Grijalva said. "Search and rescue, how to educate and prevent those deaths, targeting human trafficking all have to be part of border security."

He called on GOP leadership to advance a bill quickly.

“The speaker and his caucus have an immense responsibility not only to move a bipartisan bill forward ... but also to have the temperament and the courage to put something together that will solve this issue for the long term," Grijalva said.

Economic reforms must be built into the immigration proposals, said Rep. Beto O'Rourke, D-Texas.

“If we diverted even a fraction of the $40 billion in the Corper-Hoven amendment that militarizes the U.S.-Mexico border to facilitating trade and economic growth, we’d create millions more jobs in the United States, billions dollars more in economic activity," O'Rourke said. "Really that’s why we’re here at the end of the day, to create jobs to create economic activity, to create economic growth.”

Fronteras Desk reported that President Barack Obama met Wednesday with members of the Congressional Hispanic Caucus, and some members expressed opposition to increased border security, specifically more Border Patrol agents and more fencing.

“Having traveled most of the border last weekend I can tell you that I didn’t find a lot of support for the Wall and I didn’t find a lot of support for doubling the men in the Border Patrol," said Rep. Pete Gallego, a Democrart whose West Texas district runs along the border.

The AP reported that Obama will meet Thursday with Arizona Sen. John McCain, a Republican, and New York Sen. Chuck Schumer, a Democrat, to see what can be done to push the Senate bill in the House.

McCain and Schumer were part of a bipartisan Senate group that drafted a comprehensive bill that would create a path to citizenship for 11 million people in the U.S. illegally.