Updated

President Trump’s campaign promise to build a border wall is again starting to galvanize Washington after months of taking a back seat to ObamaCare and the investigation into Russian election meddling.

The Republican-led Congress in recent days has introduced bills that would put tens of billions of dollars toward completing a wall along the U.S.-Mexico border.

Then critics’ outrage over the wall plan intensified Thursday when The Washington Post published a leaked transcript of a call between Trump and Mexico President Enrique Peña Nieto earlier this year discussing the divisive issue.

"You cannot say that to the press," Trump told Peña Nieto in response to him saying Mexico would not pay for the wall. "The press is going to go with that and I cannot live with that. You cannot say that to the press because I cannot negotiate under those circumstances."

On Thursday, Texas Sen. John Cornyn, the chamber’s No. 2 Republican, introduced a bill that would include spending $15 billion over roughly four years on border security and a proposed wall.

The wall would combine a physical structure and technology to stop or at least slow the influx of illegal immigrants into the United States. And the bill would help pay for thousands of new judges, immigration officials and border agents that Trump wants to hire.

The bill also calls for a “massive” increase in resources at U.S. ports of entry and a national system for tracking people entering and exiting the country, according to Cornyn’s office.

“For too long law enforcement on the front lines haven’t had the tools they need to stop the flow of illegal immigration, and this bill will provide both the resources and plan to finally secure the border,” Cornyn said.

The bill is co-authored by fellow GOP Sens. John Barrasso of Wyoming, Ron Johnson of Wisconsin and Thom Tillis of North Carolina. They, like Cornyn, suggest the wall concept predates Trump and say the intent of the bill is to secure the border as a first step toward comprehensive immigration reform.

“Until our borders are fully secure, the current system will continue to reward people who enter our country illegally over those who follow the law,” Barrasso said.

Last week, Texas GOP Rep. Mike McCaul, chairman of the House Committee on Homeland Security, introduced a bill with an estimated cost of at least $15 billion that includes a physical wall, thousands more border agents and deploying the so-called “Biometric Entry-Exit System.”

“Securing our borders is first and foremost a national security issue,” said McCaul, who reportedly worked with Cornyn on the legislation. “Illegal immigrants, smugglers, and drug cartels continue to infiltrate our country. So we must quickly secure the homeland through infrastructure, technology and personnel.”

And like Cornyn’s bill, the House legislation addresses the issues of human trafficking and increases resources at ports of entry and for local law enforcement agencies.

For months Trump’s agenda has been slowed by the GOP-controlled Congress’ failed efforts to repeal and replace ObamaCare and investigations into whether the Trump campaign colluded with Russia in the 2016 presidential race.

House Minority Leader Nancy Pelosi has already seized on the border wall issue as part of her 2018 reelection bid.

“President Donald Trump and Paul Ryan are moving forward with their border wall,” the California Democrat said in a fundraising letter Saturday. “They want to break ground on construction as soon as possible so that we won’t be able to stop them. And, of course, they expect you to pick up the tab.”

The House and Senate measures also were introduced within days of Trump saying he supports a revised plan by GOP Sens. Tom Cotton of Arkansas and David Perdue of Georgia for a merit-based system for foreigners seeking legal permanent residence, or green cards, through employers.

The issue sparked an acrid exchange Thursday between Trump policy adviser Stephen Miller and CNN White House reporter Jim Acosta.