House Republican leadership is pushing for a delay to a planned markup next week of multiple immigration and border security bills as it deals with infighting between members – a move likely to upset immigration hawks keen to see action from the caucus on the historic migrant crisis at the southern border.

Punchbowl News reported Thursday that leadership has asked Judiciary Committee Chairman Jim Jordan, R-Ohio, to delay a planned consideration of as many as eight border and immigration bills next week before the April recess.

But sources told the outlet that leadership had delayed the markup until after the recess, meaning it will be more than four months since Republicans took control of the House before there is any consideration of legislation to tackle the ongoing migrant crisis at the southern border. A source familiar with the situation confirmed the Punchbowl News report to Fox News Digital.

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Jordan told Punchbowl that "we have eight pieces of legislation that we think makes sense, and we’re going to get done as soon as we can, but we’re working with the whole conference."

Republicans have little wiggle room when it comes to defections as they have just a five-seat majority in the lower chamber. While there has been consensus on the broad strokes of how the caucus should tackle the migrant crisis, deep divisions have emerged between members.

Specifically, legislation introduced by Rep. Chip Roy, R-Texas, which would allow DHS to block the entry of illegal migrants into the U.S. until there was "operational control" of the border, has seen internal Republican opposition from a small number of lawmakers.

Rep. Tony Gonzales, R-Texas, has been the most vocal opponent of the bill, calling it anti-American and claiming it bans asylum – a claim Roy has denied. Gonzales' opposition to the bill was one factor in the Texas Republican Party’s move to censure him this month.

But Republicans had campaigned on coming up with solutions to the border crisis and have already held a number of hearings at the border to draw attention to the crisis. Last year, Republicans unveiled a number of policy proposals to secure the border that they said they would advance if they took the House. Policies include finished the Trump-era border wall, expanding Title 42, modernizing technology and overhauling the asylum system.

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Since then, some Republicans – including House Speaker Kevin McCarthy – have floated the possibility of impeaching DHS Secretary Alejandro Mayorkas. That move has yet to happen, although two lawmakers have introduced articles of impeachment.

A coalition of hawkish groups, including the Heritage Foundation, Federation for American Immigration Reform (FAIR), America First Policy Institute and Numbers USA, had written to GOP leaders in February urging the party to keep its promises – and warning that resources alone were not enough and that laws needed to be changed to end loopholes.

In a statement on Thursday, Heritage Action Executive Director Jessica Anderson said border security needs to be the "top priority" for the House.

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"House Republicans have been in power for several months," she wrote. "They must immediately develop and consider a border security package that ends the asylum fraud, creates an authority to immediately expel illegal aliens, sends resources to complete the border wall, and gives border agents the personnel and tools needed to carry out their proper duties, not the mass release of illegal aliens as directed by the Biden administration. Migrants must be disincentivized from making the dangerous journey to cross the border illegally, and must not be promised any possibility of amnesty."

Anderson noted the ongoing fentanyl crisis, which is primarily smuggled across the border, as well as cartel trafficking and an increase in the number of individuals encountered on the terror watch list. While she blamed the "Biden administration’s deliberate border destruction," she also urged action from Republicans.

"The time is now – American sovereignty has been severely damaged. Heritage Action urges House Republicans to follow through on their Commitment to America and move forward on consideration of a border security package," she said.

Meanwhile, Democrats and the Biden administration have been attacking Republicans for failing to agree to border security funding requests made by the Biden administration. President Joe Biden himself has called for Republicans in Congress to support additional funding to the ports as well as pathways to citizenship for millions of illegal immigrants already in the U.S.

Fox News' Chris Pandolfo contributed to this report.