President Trump's defiance in the face of widespread criticism of his border policy has left members of his own party scrambling to find legislative fixes and increasingly fearful of midterm election backlash.

Amid mounting pressure from constituents and activists, and against the backdrop of distressing footage of migrant children separated from their parents, lawmakers are anxious for some type of speedy solution. But consensus on strategy and policy prescriptions has been hard to come by, with some members concerned about Trump's propensity to throw a wrench into the works and others arguing that he should amend the policy unilaterally.

And despite White House demands for significant legislative changes to broader immigration policy, GOP leaders have advocated for much narrower provisions. "In order to fix this problem, you can't fix all the problems," Senate Majority Leader Mitch McConnell said.

While Trump's "zero tolerance" approach to illegal immigration is a manifestation of the campaign rhetoric that mobilized his supporters in 2016, the humanitarian impact of its implementation could jeopardize Republicans' majorities in Congress.

By the time Trump arrived on Capitol Hill Tuesday night to meet with the House GOP conference, a dozen Republican senators had signed a letter urging Attorney General Jeff Sessions to suspend the border policy to give Congress time to pass a solution.

Notable among the signatories: Colorado’s Cory Gardner, who chairs the National Republican Senatorial Committee, and Nevada’s Dean. Heller, who is among the most vulnerable party members up for re-election this year. Ohio Rep. Steve Stivers, who chairs the GOP House campaign arm, also wrote a letter imploring the administration to end family separations. "If the policy is not changed, I will support other means to stop unnecessary separation of children from their parents," Stivers wrote in a Facebook post. And even longtime allies of the president, such as North Carolina Rep. Mark Meadows, have offered proposals to keep families from being split up when caught crossing the border illegally.

"The images of government officials ripping little children away from their parents is going to be another Katrina for Republicans," said Cesar Conda, former chief of staff to Sen. Marco Rubio and a close ally of Speaker Paul Ryan. "Trump should delay the separation policy for six months, and give Congress time to fix it. If they don’t, then it’s on them."

Asked whether the border issue would hurt the party’s midterm chances, McConnell argued that "it's not going to tar anybody. We're going to fix the problem."

Others did not see the need for a binary choice in addressing the crisis. "I don't think we should have to choose between enforcing the law and keeping families together. I think we can do both," said GOP Senate Whip John Cornyn. The Texas lawmaker has been working with colleagues on a legislative solution aimed at keeping families together pending their immigration hearings, and moving them ahead in the line to expedite the process. "They don't have a unified position in the White House, so what we're trying to do is demonstrate one possible solution and see if we can get the consensus we need," Cornyn added.

But forging consensus in a timely manner has often proved difficult. "Congress doesn't have a great track record of acting quickly in situations like this," Sen. Tom Cotton acknowledged. The Arkansas Republican, who is a close ally of Trump's, is advocating that Congress “overturn” the Flores Settlement Agreement, a court order that requires the government to release children from federal custody without unnecessary delay and into the care of a relative, guardian, or the “least restrictive” setting. Cotton’s solution would "allow families to be held at the border, [and] provide a little bit of extra money to the military and DHS for family housing units while those claims are adjudicated," he told radio host Hugh Hewitt. The administration supports that idea, arguing that the current law is what is causing parents to be separated from their children while they await prosecution for entering the country illegally. But overturning the order could create further complications and lead to children being imprisoned with their families. Democrats have said such a proposal is a non-starter.

Meadows, a Freedom Caucus member who is in frequent communication with the president, released legislation Tuesday that would reform asylum laws, in addition to amending the Flores Settlement. Additionally, House members are scheduled to consider two other bills later this week designed to end family separations and that also include other immigration fixes. The White House said the president backs those two measures. "He told the members, ‘I’m with you 100 percent,’” said Deputy Press Secretary Raj Shah.

Texas Sen. Ted Cruz is working on a plan that would double the amount of federal immigration judges in order to speed up the process of adjudicating illegal immigrants and processing asylum cases, of which there is a large backlog. The proposal signals the urgency among Republicans for a solution -- Cruz has long been considered an immigration hardliner, but he is also running for re-election in a border state.

Yet Trump seemed to dismiss the proposal during a speech to the National Small Business Association in Washington on Tuesday. "We don't want judges; we want security on the border," the president said. "We don't want people coming in. We want them to come in through a legal process like everybody else that's waiting to come into our country."

Trump also called for changes to legislation lawmakers have put forth. “Let's do it right. We have a chance," he said. "I don't want children taken away from parents. And when you prosecute the parents for coming in illegally, which should happen, you have to take the children away. Now, we don't have to prosecute them. But then we're not prosecuting them for coming in illegally. That's not good."

While administration officials have been working with House members on legislation, some lawmakers are concerned that the president himself could be a wild card and are looking for more clarity from him. First, they don't want to pass something he won't sign. And members depending on his base of support in their own re-election bids are hoping for him to provide them with political cover.

"The White House is going to have to be engaged in this discussion, and the president and his team need to be involved in whatever we come up with ... whether it addresses all the other elements of immigration debate or not," said Sen. John Thune, the GOP conference chair.

Other Republicans have questioned the need for any legislation. "The White House could change it in five minutes and they should. It’s a mistake. It's a change in policy by this administration," Tennessee Sen. Lamar Alexander told reporters.

Democrats, meanwhile, echoed this sentiment and declined to publicly endorse any GOP measures. "Mr. President, you alone can fix it," Senate Minority Leader Chuck Schumer said, holding up a pen. "How many times has immigration legislation passed in this Congress? Zero. ... There should be rule of law for every person who crosses the border. It is not required to separate children to enact rule of law."

Hawaii Sen. Mazie Hirono, who is herself an immigrant, was more blunt in addressing Trump: "Take that goddamn pen of yours and do away with this horrendous, inhumane policy of yours that rips children from the arms of their parents."

Democrats could pay a political price if Republicans come up with a narrow solution and they decline to come aboard. Some GOP candidates running against Democratic incumbents in the Senate have accused their opponents of supporting open borders. (All 49 Democratic senators have signed on to a measure put forth by California Sen. Dianne Feinstein that would prohibit children being separated from their families.)But for now, they are betting that public pressure will force the administration to act.

"This has caused an outcry throughout the country and has gone way beyond party," said Maryland Sen. Chris Van Hollen, chairman of the Democratic Senatorial Campaign Committee. "The public isn't going to stand for it. We'll see how this plays out."