Sen. Ted Cruz, R-Texas, announced Monday he would introduce legislation that mandates.
"All of us who are seeing images of children being pulled away from moms and dads in tears were horrified," he told reporters Monday. "This has to stop."
The "Protect Kids and Parents Act," which Cruz is introducing this week, would almost double the number of federal immigration judges, from 375 to 750, authorize new temporary shelters, with accommodations to keep families together, and mandate that undocumented immigrant families be kept together in most cases.
Cruz's bill also calls for faster processing and review of asylum cases, so that within 14 days, those meeting the legal threshold would be granted asylum, and those who don't would be sent back to their home countries.
At the White House briefing Monday, press secretary Sarah Huckabee Sanders was asked whether the president would sign legislation that allows for families to be held together, but does not include any of the president's other priorities, like funding for a border wall. She said the president wants to see a more comprehensive package that addresses a range of immigration problems. So, while the Trump administration insists that only Congress can fix this problem -- and can do so tomorrow -- it made no promise to agree to a narrow fix along the lines that Cruz is proposing, unless it is rolled into a larger immigration bill.
CBS News' Nancy Cordes and Alan He contributed to this report.