Donald Trump held a sign supporting his plan to build a wall between the United States and Mexico that he borrowed from a member of the audience at his campaign rally in Fayetteville, North Carolina March 9, 2016. Reuters

Throughout the presidential campaign, Donald Trump struck a staunch tone against undocumented immigrants while remaining resolute over building a wall along the U.S.-Mexico border. But once the New York billionaire became the president-elect, his support for the massive construction project seemed to gradually dissolve into a more moderate stance of tightening border security and increasing fencing, much to his base's dismay.

Despite Trump's softening position, many of his supporters are continuing to push for his promised "big, beautiful wall." As the White House transition team continues to fill out the cabinet, undocumented immigration opponents are slamming the president-elect for considering potential nominees who wouldn’t definitively support building a border wall.

Rep. Michael McCaul, a leading contender for secretary of homeland security, recently received a deluge of criticism from right-wing sites for not being adamant enough in his opposition to undocumented immigration. The Texas Republican has since rebuked the criticisms, calling them "incredulous and inflammatory and ... slanderous" in a Fox News interview, pointing to his track record of voting against sanctuary cities for undocumented immigrants.

McCaul then introduced a payment plan for the Mexican government to pay for the project in an op-ed for Fox News, writing, "We are going to build the wall. Period."

But critics still say McCaul is too friendly with Washington elites to follow through with his plans.

The U.S. border fence with Mexico is seen from the Mexican-facing side in U.S. territory in Brownsville, Texas, in this photo taken Nov. 17, 2016. Reuters

Executive Director of the Center for Immigration Studies blasted McCaul for being too "weak" on border security in an interview with The Hill, saying "after eight years of Obama’s presidency, the anti-borders activists have become emboldened."

"There are going to be human chains around [Immigrations and Custom Enforcement] offices. They are going to be posting the home addresses of ICE agents," he continued. "It's going to be that kind of potentially violent opposition to immigration enforcement. And I hope whoever is DHS secretary won’t go wobbly."

Dan Stein, president of the Federation for American Immigration Reform, said McCaul's ties to Republican House Majority Leader Paul Ryan and other Capitol Hill figures could deter him from pursuing the campaign promise that helped secure Trump the GOP nomination.

"This was, along with trade, the issue that allowed Donald Trump to mow down 16 other viable and talented and capable contenders in the primary process," Stein told The Hill Monday. Stein added that "nobody can bring out, in rally after rally, Americans who lost loved ones because these immigration laws were not enforced … or Americans who lost jobs because of unfair labor displacement" without fulfilling that campaign promise.

Meanwhile, Trump recently said during the kickoff to his post-election "Thank You" tour across the states that helped him win the presidential election that he still intends on building a border wall.

"Trust me, we’re gonna build a wall," Trump said. "And by the way, people are gonna come through that wall. We’re gonna have doors in that wall, but they’re gonna come through legally. And people are gonna come through on worker permits, to work the fields, we’re gonna have people, a lotta people, come through, but it’s gonna be done through a legal process. But one thing that’s not gonna come through is drugs."

Also being considered for the homeland security role are retired Marine Gen. John F. Kelly, who opposed President Obama’s efforts to close Guantanamo Bay and clashed with his White House administration over women in combat, as well as Frances Townsend, former homeland security and counterterrorism official to the George W. Bush administration. Arizona sheriff Joe Arpaio and Milwaukee County sheriff David Clarke are also reportedly being considered to fill the role, among others. Aside from McCaul, no potential candidate has outlined proposals for building a border wall.