As the issue draws continued disgust from Democrats and civil rights activists, the uncertainty underscores the difficulty Republican leaders face, particularly as the debate takes them off-message from their election-year agenda focusing on the economy.

Rev. Al Sharpton joined a group of high-profile civil rights activists Tuesday on Capitol Hill to decry the Trump administration’s practice of separating illegal immigrant children from their parents at the southern border.

“There is nothing moral or even acceptable of hearing children crying and screaming for their daddies and their mommies,” Sharpton cried, denouncing Attorney General Jeff Sessions as a “Sunday school teacher” after he cited scripture last week defending the administration’s actions.

Sharpton also charged that the administration’s policy is racist, because the Trump administration would not implement the policy at the northern border with Canada against “white children.”

“There is the inference here that because these are children of color that there's a different policy for them and that [President Trump] is playing hardball with the futures of these young people but also with the image of the United States worldwide,” Sharpton contended. “This bigoted and insensitive policy should end today.”

Sherrilyn Ifill, president and director-counsel of the NAACP Legal Defense Fund, appealed to Trump to take executive action, given the president has been eager to address other political controversies through executive order.

“He can do it. Do not be fooled by arguments that the law prevents the administration from taking action. For the last two years we have watched President Trump enjoy with relish affixing his signature to any number of executive orders, beginning with the Muslim ban. He has taken delight in acting unilaterally,” Ifill said. “He has said that he, and he alone, can solve the nation's immigration problems and yet when we ask him to step forward and take executive action as the leader of this country to protect country who are screaming for their parents, to remove America from this cloud of immorality, this embarrassment of the lack of humanity, suddenly he is unable to act?”

Responding to the backlash against the family separation policy, some Republicans have introduced narrow, stand-alone legislation meant to address the family separation policy.

Rep. Mark Meadows, the chairman of the House Freedom Caucus, has also floated an additional proposal that would remove the family separation dilemma from broader immigration reform proposals. His pitch would enact tougher scrutiny to asylum seekers while allowing children to be detained with their parents – rather than the administration’s current practice to hold them in separate detention facilities.

House Minority Nancy Pelosi joined several Democratic lawmakers on the U.S.-Mexico border near San Diego on Monday, calling the administration’s policy “barbaric” while demanding Secretary of Homeland Security Kirstjen Nielsen resign.

“This is not an immigration issue, this is a humanitarian issue. It’s about the children.” Pelosi, D-Calif., said. “We can have debates and the policy and the ‘this’ or the ‘that,’ which is wrong. But, the fundamental unifying principle for our country is this is about family and they cannot undermine the family as the American way and expect that it will have any regard for how we regard them. So, this is very, for us, it’s not political. It’s very prayerful as a matter of fact, but we do know that the answer lies with the stroke of a pen from the President of the United States.”

Democrats also assert that the GOP remedies allow indefinite detention of families.

All 49 Senate Democrats have signed onto Sen. Dianne Feinstein’s bill, the Keep Families Together Act, which prohibits officials from removing a child under the age of 18 from their parent or legal guardian at or near a port of entry within 100 miles of the border. No Republicans have cosponsored the legislation although one moderate House Republican, Rep. Mike Coffman of Colorado, tweeted support for her effort. House Democrats are working on a bill that could become a companion bill to Feinstein’s.

ABC News' Ben Siegel contributed to this report.

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