Update @ 5:47 pm ET: House majority leader Eric Cantor has confirmed that his party will take up immigration in a piece meal only approach, issuing the following joint statement authored by several Republican heavyweights:

"Today House Republicans affirmed that rather than take up the flawed legislation rushed through the Senate, House committees will continue their work on a step-by-step, common-sense approach to fixing what has long been a broken system. The American people want our border secured, our laws enforced, and the problems in our immigration system fixed to strengthen our economy. But they don’t trust a Democratic-controlled Washington, and they’re alarmed by the president’s ongoing insistence on enacting a single, massive, Obamacare-like bill rather than pursuing a step-by-step, common-sense approach to actually fix the problem. The president has also demonstrated he is willing to unilaterally delay or ignore significant portions of laws he himself has signed, raising concerns among Americans that this administration cannot be trusted to deliver on its promises to secure the border and enforce laws as part of a single, massive bill like the one passed by the Senate."

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Former President George W. Bush was back in the spotlight Wednesday morning, appearing at an opening for a center with his namesake in Dallas, Texas. He tackled immigration just as lawmakers in Washington were preparing to do the same. But while Bush’s message was based on what appeared as a sincere hope that comprehensive immigration legislation would move forward, the House doesn’t appear likely to push through a Senate bill passed less than two weeks ago.

Bush offered his remarks at a naturalization ceremony–which inaugurated the George W. Bush Institute. In welcoming a group of immigrants who had just attained citizenship, Bush recognized that for many of those involved, it had been a long process, adding that he was honored to call those in the ceremony his fellow Americans. He then moved to address the broader question of immigration reform. "I don’t intend to get involved in politics, or specifics of policy," said the former president. "But I do hope there is a positive resolution to the debate."

But conservative voices remain varied on immigration. A joint editorial, penned by William Kristol and Rich Lowry, appeared in both the Weekly Standard and National Review; both are respective editors at the two leading conservative publications, with a far reach. The editorial, which stipulates that there is "no rush to act on immigration," concludes that passing the Senate version of the bill "would be worse public policy than passing nothing."

House Speaker John Boehner, R-Oh., meanwhile, is pressed to convince his colleagues to support a comprehensive immigration bill or piece-meal legislation–and it appears he’ll push for a series of stand-alone bills if he’s not satisfied that a bigger bill will first secure the border. Boehner continues to maintain his position that he will not back the current Senate bill. But that gamble may prove difficult if the Republicans want to keep the House next year.

As House lawmakers meet to figure out what to do next, the Congressional Hispanic Caucus is also meeting with President Obama Wednesday to talk about immigration reform. One member, Filemon Vela, D-Tx., resigned from the caucus last week, in protest of the Senate version of the bill’s stipulation for increased border fencing and surveillance.