(CNN) Republicans are growing anxious over President Donald Trump's policy to break up families at the border -- and now even his closest allies are trying to help find a way out of a growing political crisis.

With the White House refusing to reverse the practice and demanding Congress step into the fray instead, one of Trump's closest allies is offering a narrowly targeted bill seeking to ensure immigrant parents are not separated from their kids while they are in Department of Homeland Security custody.

Rep. Mark Meadows, the head of the conservative House Freedom Caucus, is offering a new bill that that would allow children to be detained indefinitely with their parents, would raise the threshold for asylum seekers and is a far more limited in scope than two other pieces of legislation GOP leaders hope to bring to the floor this week.

The Meadows bill is the latest sign that Republicans across the spectrum are eager to find a quick legislative fix to stanch the bipartisan uproar amid images of young children being housed in detention facilities along the southern border with Mexico. But the party is badly divided on how to respond -- and whether Trump should just fix the matter himself.

"The President's agenda of cracking down on illegal immigration is critical, and yet many of us, including the President, agree: there is a better way to solve the complications of illegal immigration proceedings than separating children from their parents at the border," Meadows said in an email to CNN. "We need to better enforce our immigration laws, but we can do so while keeping parents and children together."

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