From left, Sens. Thomas R. Carper (D-Del.), James M. Inhofe (R-Okla.) and Barbara Boxer (D-Calif.) announce a bipartisan transportation funding bill Tuesday on Capitol Hill. (Ashley Halsey/The Washington Post)

Breaking a deadlock that threatened federal highway funding, a bipartisan coalition of senators on Tuesday introduced a six-year bill that would boost overall spending on U.S. roads and bridges.

Working against a July 31 deadline, the senators acknowledged that it will be an uphill effort to corral their Senate colleagues and the House to pass a bill.

“There are three other committees, and both sides of the aisle, and they have to do their part as well,” said Sen. Barbara Boxer (D-Calif.), her party’s senior member on the Environment and Public Works Committee, who added that negotiations over the bill almost collapsed last week. “I think we need to do even more, but what a wonderful start this is.”

Boxer joined Sen. James M. Inhofe (R-Okla.), the committee’s chairman, and Sens. David Vitter (R-La.) and Thomas R. Carper (D-Del.) in a show of bipartisan strength.

“This is an area where Barbara and I love each other. This is one area where we can, because the alternative to a big, long-term bill is to have short-term fixes,” said Inhofe, who discounts global warming and is at loggerheads with Boxer on environmental issues.

The emergence of a bill won immediate praise from states and the construction industry, which have felt shackled by the uncertainty of a series of short-term funding extensions.

“It’s a message to all members of Congress that they shouldn’t let perceived obstacles rule the day,” said Pete Ruane, president of the American Road and Transportation Builders Association. “Transportation investment is a core federal responsibility. It’s time to transcend politics and do the right thing for America.”

The Senate bill sets the stage for a dramatic July. In the middle of their summer construction season, state highway officials already have been warned that federal payments are at risk once current funding expires July 31.

As recently as last week, many in the House seemed resigned to another short-term extension of funding at current levels. If that comes to pass, it will be the 34th time in more than six years that states have been left in the lurch, pondering whether to launch multi-year projects without the assurance that federal money will come through to pay for them.

The six-year bill would increase highway spending by almost 13 percent over the current level, bumping it up by more than $2 billion each year. It includes a new program to spread more than $2 billion a year among states to invest in improvements for freight facilities that move goods and products.

It further streamlines project approval, whacking away at the federal red tape that state officials say has slowed the process. It holds flat at $819 million the money for pedestrian and cycling improvements and for roadway landscaping, spending that has drawn the ire of conservatives who believe the cost of those tasks should be left to the states.

And for all the bipartisan fanfare surrounding Tuesday’s announcement, muscling a bill through the Senate and House in just five weeks meets only half of the challenge. Looming larger — as it has for several years — is the question of how to pay for it.

Failure to address a multibillion-dollar deficit in the Highway Trust Fund is the reason Congress has been able to pass only one genuine long-term bill to fund highways and transit systems so far this century.

That bill expired in 2009, to be followed by a series of extensions, and a two-year bill in 2012 that was funded with a series of improvisations, sidestepping the question of how to replenish a trust fund reliant on rapidly dwindling gas taxes.

A bill that increases current funding by about 3 percent a year puts the House and Senate committees that must come up with the cash in a bind just a week after those committees appeared no closer to resolving the issue.

At a hearing last week, Senate Finance Committee Chairman Orrin G. Hatch (R-Utah) said that finding the money “seems insoluble,” but he said he was determined to do it nonetheless.

House Ways and Means Committee Chairman Paul Ryan (R-Wis.) admitted that Congress had dodged the issue, but other than saying no to an increase in the 18.4-cent federal gas tax, he offered little in the way of suggestions.

The two-year authorization bill that expired in 2014 also was introduced before the financing committees had come up with the means to pay for it.

“There’s a cart-and-horse issue here, and sometimes it’s better to say what you’re buying before you write the check,” said a senior staff member who helped craft the bill. “Our view is that you spell out a framework of what you get for the money instead of talking about everything in abstract.

The bill’s funding falls short of a six-year White House proposal that would raise annual funding for transportation by almost $25 billion.

Since 2008, lawmakers have transferred $62 billion in general tax revenue to bolster the sagging trust fund. In the current fiscal year, the fund is projected to take in $39 billion for highways and transit, while Congress has authorized $52 billion in spending.

The Congressional Budget Office last week said that to maintain the current level of spending, Congress should expect to transfer $11 billion from the general fund next year. The sum transferred would grow to $22 billion by 2025.

Unlike the House, where the Transportation Committee handles all modes of transportation, the Senate divides types of transportation among three committees. The bill that emerged Tuesday came from the Environmental and Public Works Committee, where Inhofe is chairman and Boxer is the senior member of the minority party. That committee’s domain is highways, the Banking Committee handles transit systems, and the Commerce Committee is responsible for buses and railways.

Although highways receive about 85 percent of the spending in a transportation bill, the banking and commerce committees would contribute to a bill before it reached the Senate floor.

The Inhofe-Boxer proposal for highways would spend about $350 billion on roadways over six years. Neither the Senate Banking Committee nor the Senate Commerce Committee has acted, but it is estimated that the additional cost for transit, buses and railroads could add more than $90 billion to the package.

Despite the challenges, Inhofe said Tuesday that the bill could move quickly.

Senate Majority Leader Mitch McConnell (R-Ky.) “is anxious to get this out,” Inhofe said. “It’s going to be very soon.”