(Jenny Starrs/The Washington Post)

Republicans are showing increasing reluctance to build a wall on the U.S.-Mexico border, even as President Trump prepares to ask Congress to include billions for one of his signature campaign promises in his first budget proposal since taking office.

Key GOP senators expressed concerns this week about who would foot the bill for the wall, with some bluntly voicing doubts that Mexico will cover it, as Trump has vowed. Even among those open to the idea of a wall, many spoke about it in less than enthusiastic tones.

“I don’t care at all as long as Mexico’s paying for it — it’s neither here nor there for me,” said Sen. Jeff Flake (R-Ariz.), whose state has a nearly 400-mile border with Mexico. “But if we’re paying for it, it’s a significant concern.”

On Thursday, Trump will unveil a budget plan that calls for about $1.5 billion in immediate funding to start planning and building a wall along the Mexican border — and another $2.6 billion to fund border security next year.

The emerging split is likely to add tension to upcoming budget negotiations designed to keep the government open past the end of April. Democratic leaders have said they are prepared to block that interim spending bill if it contains funding for the wall. That could leave Republicans having to choose between helping Trump fulfill one of his core promises and securing enough votes to avoid a shutdown.

What's getting cut in Trump's budget

“It may not be possible to do everything we want to do by April 28,” said Sen. John Cornyn (R-Tex.), noting the date through which the government is funded. Asked whether he supports constructing a wall, the second-ranking Republican senator said, “I support border security, but I think we need a little more definition of exactly what the plan is.”

Trump on Thursday will unveil his first official budget proposal to fund federal agencies in the 2018 fiscal year. Trump is also expected to ask Congress to authorize additional money for the wall as part of a separate spending package for border security and military readiness.

In the Senate, where Republicans hold a narrow 52-48 advantage over the Democratic Caucus and funding bills need to clear 60-vote procedural thresholds to pass, there is little eagerness among Republicans to dive quickly into erecting a wall amid uncertainty about how it will be financed. It could cost between $8 billion and $25 billion, according to some estimates.

Asked if he thinks Mexico will pay for the wall, Sen. John McCain (R-Ariz.) responded simply: “No.” His comments echoed similar skepticism Senate Majority Leader Mitch McConnell (R-Ky.) has voiced in the past.

Trump has said he wants to put up a wall to curtail the flow of illegal drugs and undocumented immigrants into the United States. But even wall backers said they don’t view a physical barrier as the only line of defense.

“I believe a border wall is part of our security needs, but that alone isn’t going to achieve the goal,” said Sen. Marco Rubio (R-Fla.).

Rubio acknowledged that building a wall means forcing some Americans to sell private land along the border to accommodate construction. That process, known as eminent domain, allows the federal government to require land owners to choose between accepting an often below-market value price for their home or risk having the government seize the land without permission.

(Video: Jenny Starrs/Photo: Jabin Botsford/The Washington Post)

Senate Minority Leader Charles E. Schumer (D-N.Y.) and other top Democrats warned GOP leaders this week that they are willing to risk a shutdown fight to block the wall.

“I think that wall would be an awful symbol for the United States,” said Sen. Richard J. Durbin (D-Ill.), Schumer’s top deputy. He added: “It’s really an issue that we feel strongly about in the Democratic Caucus.”

Schumer is betting that Republicans will take the blame if the border wall fight gets that far. But that’s a perilous proposition that could backfire on them.

Some Republicans believe that combining the wall request with other military spending could be an effective way to pressure Democrats to vote for the bill. The logic, according to GOP aides, is that most lawmakers will feel uncomfortable voting against the wall if the funding is combined with money necessary to help troops fighting in Iraq and Afghanistan.

“I’m amused by the Democrats apparently warming up to the idea that threatening to shut down the government’s a good idea,” McConnell told reporters this week.

At a congressional GOP retreat in late January, McConnell and House Speaker Paul D. Ryan (R-Wis.) said they were prepared to move ahead with legislation to provide $12 billion to $15 billion to pay for a wall. But they left rank-and-file members wondering whether the costs would be offset by spending cuts elsewhere in the government, unnerving fiscal conservatives.

The White House created uncertainty that same day as it raised the prospect of taxing imports differently as a technical way of securing payment from Mexico, but the administration later stressed that position was not final.

Since that time, Republican senators have treaded lightly around the wall issue.

“I’ll make comments regarding the budget after I see it,” Sen. Bob Corker (R-Tenn.), the chairman of the Senate Foreign Relations Committee, said when asked earlier in the week how much of a priority building a wall was to him.

“He’s doing his research — I definitely support that,” was as far as Sen. James Lankford (R-Okla.) would go when asked whether he supports Trump’s calls to build a wall.

In the House, Republicans hold a wider advantage over Democrats and need only a simple majority to pass legislation. Still, the idea of a wall is not without its GOP critics there.

Rep. Will Hurd (R-Tex.), whose district spans more of the border than any other, called a wall “the most expensive and least effective way to secure the border” in a January statement.

Trump signed an executive order that month calling for the “immediate construction of a physical wall.” Mexico’s government has said it will not pay for a wall.

During the campaign, Trump’s supporters would regularly break into enthusiastic chants of “Build that wall!” at rallies when the candidate would discuss his plans for border security and immigration.

But in the Senate, it’s increasingly clear that is not a widely shared sentiment.

“My focus is on defense spending. Not ‘the fence’ — defense,” said McCain.

Ed O’Keefe contributed to this report.