President Trump’s promise to find $1 trillion for infrastructure ran headlong into the senior senator from Wyoming, who said on Wednesday that the White House plan to raise private money for roads and bridges wouldn’t do much to help his rural state.

Sen. John Barrasso (R), who chairs the Senate Committee on Environment and Public Works, represents a state with fewer inhabitants than Washington, D.C. His state's capital, Cheyenne, has a population not much larger than that of Rocky Mount, N.C.

“Funding solutions that involve public-private partnerships, as have been discussed by administration officials, may be innovative solutions for crumbling inner cities, but do not work for rural areas,” Barrasso, who figures to play a central role in any infrastructure plan, said at a hearing Wednesday.

Trump has made infrastructure investment a focal point of his presidency, but the only substance to support his goals thus far has been a 10-page white paper that emerged in the final days of his campaign.

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Written by Wilbur Ross and Peter Navarro, the paper says that by providing investors with an 82 percent tax credit, private money can be raised to pay for roads, bridges, transit and other critical infrastructure needs. (Ross is Trump’s nominee for commerce secretary; Navarro is head of the president’s National Trade Council.)

The challenge to that approach is that private investors will want a return on their money beyond the tax credit, so only through tolling or other methods of raising money will their investments pay off. That makes high-volume urban areas attractive, while less-populated areas would be unlikely to see private cash.

Senators anticipate that the Trump administration will expand its infrastructure plan beyond the Ross-Navarro paper, and that Transportation Secretary Elaine Chao will work with Congress to craft a more comprehensive approach to funding transit, roads and bridges.

In Barrasso’s home state, cattle outnumber people 2 to 1. That ratio is slightly lower in Idaho and much higher in three other states — Montana, North Dakota and South Dakota, four states that were represented at Wednesday’s hearing by William Panos, director of Wyoming’s Department of Transportation.

“Public-private partnerships and other approaches to infrastructure investment that depend on a positive revenue stream from a project are not a surface transportation infrastructure solution for rural states,” Panos said. “The traffic volumes on projects in rural states are low, and it’s almost never feasible from revenue generation.”

Finding any additional revenue, let alone the $3.7 trillion estimated to meet infrastructure needs by 2020, has been the congressional challenge since the existing source, the gas-tax-funded Highway Trust Fund, began failing to meet the need. The funding for the current transportation bill was achieved from sources that have been described as “gimmicks” and “funny money.”

Panos said finding new revenue sources to replenish the trust fund is important if the federal government wants to continue spending for projects in states such as his.

“The Highway Trust Fund and the programs it supports are critical to maintaining and improving America’s surface transportation infrastructure,” Panos said.

In the House last week, Rep. Peter A. DeFazio (D-Ore.) proposed an increase in the 18.4 cent-per-gallon federal gas tax, which has not been raised since 1993, a hike he said would increase the cost per gallon by 2 cents.

A gas tax increase has been supported by the U.S. Chamber of Commerce and big fuel users such as FedEx. But many members of Congress have been loath to embrace any measure that would increase taxes.

At the Senate hearing Wednesday, Sen. Thomas R. Carper (D-Del.) invoked his father’s mantra: “Things that are worth having are worth paying for.”