Rep. Marsha Blackburn (R-Tenn.) on Wednesday pitched her House Republican colleagues on legislation to defund President Barack Obama’s controversial policy of deferring deportation for some illegal immigrants, and said she’s hearing positive feedback on her idea.

“We had a good immigration discussion,” she told TheBlaze of her talk with GOP colleagues Wednesday morning. “I have to tell you, I think that members locked onto the fact that, yes, that 2008 law is a problem, but what is more problematic and what has accelerated the rate of illegal cross-border trips… is this executive order, the DACA.”

U.S. Rep. Marsha Blackburn (R-Tenn.) is seeking support in the House for her bill to defund President Obama’s deferred deportation policy. Alex Wong/Getty Images

The 2008 law is the Trafficking Victims Protection Act, which prevents the government from more quickly deporting illegal immigrant children from Central America. Republicans seem mostly agreed on the need to fix that law, and a GOP working group created by House Speaker John Boehner (R-Ohio) announced Wednesday that it would seek legislation to do that, among other things.

What wasn’t in the GOP plan, however, was a proposal to defund Obama’s Deferred Action for Childhood Arrivals policy, or DACA. Many Republicans have said Obama’s 2012 policy is acting as a magnet that has lured roughly 60,000 children into crossing the southern U.S. border.

Blackburn said about a dozen Republicans signed onto her bill immediately, and that many other offices have expressed an interest in becoming cosponsors.

A key question in the House is whether the Boehner-led initiative will allow language on DACA to be considered or included on legislation that’s being prepared. As of Wednesday, it wasn’t clear how Boehner would proceed in the effort to pass a bill, and whether any amendments might be considered when it hits the floor as early as next week.

Blackburn didn’t make any predictions about the fate of her language in the House, but said it’s important to start the discussion about terminating DACA as a response to the border crisis.

“I’ve been very pleased with the amount of awareness and the way people have responded to the bill,” she said.

She also told TheBlaze that the best leverage the House will have over Obama is the border bill, since Obama has asked Congress to provide increased funding to cope with the crisis. Obama asked for $3.7 billion, but Republicans roundly criticized the bill as something that would spend money to deal with the tens of thousands of children, but would do nothing to stop the wave of immigrants.

In addition to support in the House, Blackburn has support in the Senate from Sen. Ted Cruz (R-Texas), who proposed identical legislation on DACA earlier this month.

“The only way to stop the border crisis is to stop President Obama’s amnesty,” he said Tuesday. “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.”

Sen. Jeff Sessions (R-Ala.) also indicated support for the idea in a late Wednesday statement. Sessions said the Boehner initiative outlined earlier in the day didn’t recognize Obama’s role in creating the crisis.

“The president’s continued determination to carry out this nullification remains the singular obstacle in the way of restoring lawfulness,” Sessions said. “It is therefore odd that the House working group did not mention President Obama even once in their released findings. Indeed, they made no mention of the president’s threat of sweeping new executive actions.”

In calling for a tougher House proposal, Sessions also said the proposal would appear to allow “unjustified claims of asylum to overwhelm our system,” and appeared to do little to rebuild border enforcement efforts.

Several Democrats have responded to the border crisis by saying the House should simply pass the Senate-passed immigration bill. But Republicans like Sen. Jeff Sessions (R-Ala.) have said that bill would only expand immigration further and cost American citizens jobs, in addition to attracting even more illegal immigrants.

Blackburn said in discussions with her constituents, the border crisis is souring people even more on the Senate-passed bill.

“What I have heard from many people is it has not furthered the drive for immigration reform, it has done quite the opposite,” she said.