Republicans in the House and Senate introduced several new legislative proposals aimed at fixing the humanitarian crisis at the southern U.S. border — including plans to enforce the border, speed up the process of deporting illegal immigrant children, and remove the incentives that the GOP believes are enticing Central American children to cross into the United States.

Republicans say the Obama administration has created the impression that children can stay in the U.S. once they cross over through its deferred deportation policy against younger immigrants. And in fact, many can stay — government officials have estimated that about half of the children crossing over may have a legitimate asylum claim, and that nearly half never show up for the deportation hearing.

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Sen. Ted Cruz (R-Texas) on Thursday offered a new bill that would ensure President Barack Obama’s policy of deferred action for childhood arrivals does not include recent child immigrants. As of today, DACA applies only to children brought into the U.S. before 2007, but Cruz said Congress needs to make sure the policy is not expanded.

“The only way to stop the border crisis is to stop President Obama’s amnesty,” Cruz said. “If we do not put an end to its expansion – to the promise of amnesty that is the reason so many are coming – then more little boys and girls will be trafficked, abused, and even killed.”

Cruz said he would propose another bill next week to ensure the faster deportation of immigrant children, an issue that is the subject of several other bills proposed Thursday.

On the issue of enforcement, Rep. Steve King (R-Iowa) and several other House Republicans proposed a resolution that supports the use of the National Guard to help secure the border in Arizona, California, New Mexico and Texas.

While this is a non-binding resolution, passing it would send the signal that the House supports an increased National Guard presence, an action that the Obama administration has not taken so far.

Earlier this month, Department of Homeland Security Secretary Jeh Johnson indicated the administration believes this option is too expensive. But Republicans like King — and House Speaker John Boehner (R-Ohio) — say the Guardsmen may be needed temporarily.

“Right now there is an incentive for illegals to continue to pour across our border, and the only way to discourage them is to seal our border and send them back,” King said. “Therefore we call upon the southern border Governors to call up their National Guard units to secure the border.”

These bills and many others were introduced Thursday, even as a House working group was trying to come up with a border proposal. Unlike President Obama’s request for $3.7 billion, the House bill was expected to cost less, include spending offsets, and include legal changes making it easier to deport children from Central America.

Cruz and King were joined by several other Republicans with their own border bills on Thursday.

In the Senate, Arizona Republicans John McCain and Jeff Flake introduced their previously announced bill, the Children Returning on an Expedited and Safe Timeline Act, or the CREST Act. That bill requires faster deportation for Central American children and all other illegal immigrants trying to cross into the United States.

It also requires mandatory detention of all children until their immigration hearings are held, and adds more judges to handle an increased caseload.

“This crisis will continue until the parents who paid thousands of dollars to smuggle their children north to the United States see plane-loads of them landing back at home – their money wasted,” McCain said.

In the House, Rep. Jason Chaffetz (R-Utah) proposed the Asylum Reform and Border Protection Act, along with Rep. Lamar Smith (R-Texas). That bill would speed up the deportation of immigrant children, and make it harder for them to claim “credible fear,” which allows them to stay in the United States.

“Too many are finding ways to game the system,” he said. “By strengthening standards for those who claim ‘credible fear’ we can expedite the removal process.”

Chaffetz’s bill would also ensure U.S. border agents have access to border lands protected by environmental laws.

Several other members proposed bills dealing with the border, including:

— Rep. John Carter (R-Texas) proposed his own bill to provide for the expedited removal of immigrant children.

— Rep. Michael Burgess (R-Texas) proposed legislation that would reduce the amount of U.S. foreign aid for El Salvador, Guatemala and Honduras based on the number of unaccompanied immigrant children who are placed into the custody of the U.S. government.

— Rep. Adrian Smith (R-Neb.) proposed a bill requiring governors to be notified whenever unaccompanied immigrant children are placed in their state — a similar bill was proposed by Sen. Mike Johanns (R-Neb.).

— Rep. Pete Olson (R-Texas) proposed a related bill that would require consultations with states before federal funding is awarded to build housing facilities for immigrant children.

— Rep. Kristi Noem (R-S.D.) proposed a bill with several other members to require new strategies to prevent child trafficking.

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