(CNN) Some Senate Republicans are openly admonishing the Trump administration for its practice of separating families at the border , while GOP leadership is considering whether there's legislation they can pass to fix the roiling situation along the US southern border.

Sen. John Cornyn of Texas, the second-ranked Republican in the chamber, said a small group of senators are working on legislation to address the child separation issue, with the possibility of having something ready as soon as Tuesday and a vote on it as soon as this week.

"The solution is up to us. If Democrats don't want to work with us to solve the problem, shame on them," Cornyn told reporters. "We think we're coming up with a reasonable way to solve the problem of family separation that's humane and compassionate but also allows the government to enforce the law."

While Cornyn's comments appeared to respond to President Donald Trump's request for a congressional solution, other Republicans in the Senate sharply criticized the President and said he could address the separation of families now.

"The administration's current family separation policy is an affront to the decency of the American people, and contrary to principles and values upon which our nation was founded," tweeted Sen. John McCain, an Arizona Republican who's been recovering from cancer treatment in his home state. "The administration has the power to rescind this policy. It should do so now."

"The administration's decision to separate families is a new, discretionary choice," said Nebraska Sen. Ben Sasse, another one of several high-profile Republicans to speak out in recent days. "Anyone saying that their hands are tied or that the only conceivable way to fix the problem of catch-and-release is to rip families apart is flat wrong. There are other options available to them."

Whether the blistering statements will manifest themselves into legislation remains to be seen. Such action would require GOP members to directly defy Trump, something the party has been hesitant to pursue in an election year. And the Senate has already had a bruising fight over immigration earlier this year that resulted in no legislation advancing, making a possible return to debating the subject all the more significant.

But saying nothing no longer seems like an option. After a weekend of lawmaker visits to detention centers, images of children behind metal fencing and a growing awareness of what President Donald Trump's "zero-tolerance" policy actually means along the border, a small number of Republican senators are calling for changes.

Sen. Orrin Hatch, a Republican from Utah and the longest serving GOP senator in history , called the practice of separating families at the border "wrong."

"While I recognize the difficulty the last two administrations have faced with regard to families illegally crossing the border, I wholeheartedly agree with the President's comments that a policy that leads to separating children from their families is wrong," Hatch said. "I am working with colleagues in both houses on a path forward that recognizes the need for compassion for children and families without incentivizing illegal border crossings. That solution can and should be bipartisan."

"The time is now for the White House to end the cruel, tragic separations of families," Alaska's Republican Sen. Lisa Murkowski said in a statement. "They are not consistent with our values."

"While I firmly support enforcing our immigration laws, I am against using parental separation as a deterrent to illegal immigration," tweeted GOP Sen. Pat Roberts of Kansas. "My concern, first and foremost, is the protection of the children."

Republican lawmaker reaction to family separations grew more intense over the weekend. Republican Sens. Jeff Flake of Arizona and Susan Collins of Maine sent a letter to the Department of Homeland Security and the Department of Health and Human Services demanding answers about the practice.

"The United States will not be a migrant camp and it will not be a refugee holding facility, it won't be," Trump said Monday. "You look at what's happening in Europe, you look at what's happening in other places, we can't allow that to happen to the United States, not on my watch."

Louisiana Republican Sen. John Kennedy described the situation this way: "I think the whole thing is a hot mess."

"I support the practice of arresting people who break the law," he said, but he added that he would like children to stay with their parents. "That would be my strong preference."

In the House, Republican lawmakers could vote on legislation as soon as this week that would address a host of immigration issues. A compromise piece of legislation would provide Trump with his border wall and give recipients of the Deferred Action for Childhood Arrivals program, a legal status that would allow them -- if they meet certain criteria --to someday apply for citizenship.

The House bill would also overturn a court settlement and allow children to remain in DHS custody indefinitely. The change would allow families to stay together, but only while in DHS custody. If the parents are criminally prosecuted -- as is the practice with zero tolerance-- parents and children would still be separated.

House moderates have sought ways to further bolster protections to ensure that families can stay together.

"That's an issue of great concern to me. And we're still looking for ways to do more to keep families together in this legislation," Florida Republican Rep. Carlos Curbelo told reporters last week.