Washington (CNN) President Donald Trump's plan to build a wall on the border with Mexico is facing a major problem: A wall of resistance from his own party.

A growing number of congressional Republicans are objecting to the cost and viability of a proposal that was a rallying cry for the billionaire businessman during his insurgent campaign. Interviews with more than a dozen GOP lawmakers across the ideological spectrum suggest Trump could have a difficult time getting funding for his plan approved by Congress.

Many bluntly told CNN they'd likely vote against any Trump plan that is not fully offset with spending cuts, while others questioned whether Trump's vision would adequately resolve the problems at the border.

"If you're going to spend that kind of money, you're going to have to show me where you're going to get that money," said Alaska Sen. Lisa Murkowski, a key swing vote who has already broken with Trump over his nominee for secretary of education.

"I don't see how you can get a bill like that through (Congress) without offsets," she added. "I don't see how that's possible."

Trump's wall already faces legal hurdles given the likelihood that it could spawn lawsuits at the border. But if Congress doesn't go along with his funding plan, it could effectively stall Trump's proposal right out of the gate. House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell said last week that the cost could range from $12 billion-$15 billion, while Ryan suggested that the project may not be fully offset with spending cuts, saying the wall is "a national security priority."

Sen. John Cornyn, the No. 2 Senate Republican who represents the border state of Texas, was deeply skeptical about whether a wall alone would be enough to deter immigrants from entering the country illegally. And he issued a stark warning to Trump.

"I have concerns about spending un-offset money, which adds to the debt, period," Cornyn said bluntly when asked about the wall. "I don't think we're just going to be able to solve border security with a physical barrier because people can come under, around it and through it."

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Trump has increasingly said that Congress would fund the wall initially but would later be reimbursed completely by Mexico. But prominent Republicans say flatly that they don't think Mexico will pay the United States back -- and Mexican leadership has repeatedly said the same -- meaning that taxpayers would be left holding the bag.

"No," Arizona Republican Sen. John McCain said when asked if he thought Mexico would reimburse the United States for the wall. "It's not a viable option."

McCain added: "If you only build a wall, only a 'wall,' without using technology, individuals, drones, observations, etc., you're not going to secure the border."

Trump still has time to convince his party to go along, especially if he provides more details on his plans, given Republicans are largely united behind calls for more robust border security. And some GOP senators, like Ron Johnson of Wisconsin, suggest they're open to paying for the wall even if it's not offset by spending cuts.

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Behind the scenes, the Trump administration has tried to shore up support. John Kelly, the new secretary of Homeland Security, began to discuss with lawmakers this week his border security plans, sources said, but senators reported there were few details on the specifications of the wall.

The Trump administration is working on a supplemental funding package to pay for border and national security, but that work has stalled as the Senate moves slowly to confirm Trump's pick of Rep. Mick Mulvaney as his budget director.

Still, Trump wants to move quickly on the wall, within the first quarter of this year. And even if he asks for spending cuts to pay the wall, sources on the House and Senate appropriations committees say finding upwards of $15 billion in reductions would be extraordinarily difficult, especially in the middle of the fiscal year.

After last week's party retreat in Philadelphia, many Republicans also voiced concerns that there isn't enough focus on reducing the debt and deficit -- especially as Trump pushes Congress to green-light new infrastructure projects aside from the wall.

"I don't want to see any spending, additional spending on anything done that is not paid for," said Sen. Bob Corker, Republican of Tennessee, when asked about the wall. "We have got a huge fiscal problem right now -- $20.355 trillion in debt projected to add $9.7 trillion over the next 10 years. And I'm concerned that when I left the retreat last week there are so many things that people are talking about spending money on and at the same time lowering the amount of revenue. And it's a recipe for disaster."

Corker added he was concerned about a number of proposals that will add to the debt -- not just the wall.

A White House spokesperson did not respond to a request for comment, but the administration has been vague on its plans. White House spokesman Sean Spicer suggested last week that the administration was considering imposing a 20% tax on Mexican imports to pay for the wall, but hours later said it was one of a list of ideas after Republican senators pushed back on that proposal.

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In one of his first moves as president, Trump took executive action to order the construction of the wall, with Spicer saying "his goal was to get the project started as quickly as possible" with existing funds and then "move forward and work with Congress on an appropriation schedule." Spicer added that the American taxpayer will be "wholly respected."

But lawmakers will need more convincing to agree to pay up.

Sen. James Lankford of Oklahoma is skeptical that Trump will get Mexico to pay for the wall, meaning he thinks Congress needs to find spending cuts to pay for the plan.

"I don't count on Mexico to pay for our national security," Lankford said. "It's the responsibility of every nation to take care of their own security."

Sen. Lamar Alexander of Tennessee, a close McConnell ally who sits on the Senate Appropriations Committee, said: "Everything we spend we need to find a way to pay for."

In the House, Trump could also face a wall of resistance from deficit hawks like Rep. Justin Amash of Michigan.

"It looks like they're going to blow up our budget," Amash warned.