Earlier in the day, counselor to the president Kellyanne Conway attempted to distance the Trump administration from the rise of migrant children separated from their parents at the Mexican border.
A new Trump administration policy, which went into effect in May, sought to maximize criminal prosecutions of people caught trying to enter the US illegally.
"If the Democrats are serious, and if a lot of Republicans are serious, they'll come together", she said.
On Saturday, Trump was more direct: "Democrats can fix their forced family breakup at the Border by working with Republicans on new legislation, for a change!"
On 'Fox & Friends, ' Homeland Security secretary says the need for action on border security is clear.
Steve Bannon, President Trump's former White House senior adviser, said Sunday a wall at the southern border would solve the problem of separating children from parents who illegally enter the United States.
Appearing on NBC's "Meet the Press" Conway said, "As a mother, as a Catholic, as somebody who's got a conscience ..."
She added, "Let me just tell you that nobody likes seeing babies ripped from their mother's arms, from their mother's wombs, frankly, but we have to make sure that DHS's laws are understood through the sound byte culture we live in". She said the U.S. government "should not be in the business of warehousing children in converted box stores or making plans to place them in tent cities in the desert outside of El Paso".
"It is inconsistent with our American values to separate these children from their parents unless there's evidence of abuse or another very good reason", she said.
O'Rourke denounced the "inhumane separation of children from their parents" and the conditions at the tent camp, and complained that migrants who present themselves at ports of entry, seeking legal asylum, are being denied due process.
For more than a decade, even as illegal immigration levels fell overall, seasonal spikes in unauthorized border crossings had bedevilled US presidents in both political parties, prompting them to cast about for increasingly aggressive ways to discourage migrants from making the trek.
"Without him coming to Capitol Hill on Tuesday, I don't think we'd have that sort of maximum pressure, if you will, to get us across the goal line, and I anticipate on Tuesday that he's going to be the leader he is and we're going to get something passed out of the House", said Mr McCaul. We need border security.
"They call it 'zero tolerance, ' but a better name for it is zero humanity, and there's zero logic to this policy", said Senator Jeff Merkley of Oregon. Karl pushed back on Bannon's claim that Martin Luther King, Jr. would be proud of the effects of Trump's policies on minorities.
Trump has steadfastly tried to deflect blame for the separation of children from their parents, consistently dissembling about why it is occurring.
Democrats have introduced legislation to force Trump's hand.
Since the policy was enacted both Democrats and Republicans have spoken out against Trump and his administration.
President Trump "has not always told the truth", host Jonathan Karl said while recalling Bannon's time in the White House, but Bannon disagreed.
"She did not know what was going on", said paralegal Georgina Guzman, recalling their conversation at a federal courthouse in McAllen, Texas.