Transportation Secretary Anthony Foxx said that Congress’s gimmicks to extend transportation funding are like money found under a mattress. “We’re running out of mattresses,” he said. (Andrew Harrer/Bloomberg)

With the ritual hand-wringing and finger-pointing familiar to such events, the House on Tuesday voted for the 33rd time since 2008 to extend transportation funding, again dodging the issue of how to pay for highways and transit in the long term.

The two-month extension leaves state and local transportation officials in the lurch as they plan for the balance of the summer construction season and ponder whether to embark on long-term projects that require the certainty of federal funding.

With funding set to continue through July 31, they face the possibility that cash from Washington could be rationed — or cut off — when the extension expires.

“Unfortunately, we were unable to reach an agreement on a long-term bill, so we are left with a short patch,” Rep. Bill Shuster (R-Pa.), chairman of the House Transportation Committee, said on the floor during debate. “A long-term transportation bill will continue to be a top priority for this committee.”

“Here we are again, another short-term patch,” said Rep. Peter A. DeFazio (Ore.), the ranking Democrat on Shuster’s committee. “It’s a heck of a way to run a nation. It is embarrassing.”

House Democrats followed the vote by introducing the Obama administration’s $478 billion, six-year transportation bill, which would increase annual spending. It has little chance of winning approval in the Republican-controlled Congress.

“We now have something to work with,” DeFazio said. “I think it’s important to put it down as a marker. Let’s negotiate section by section.”

Shuster has been in discussions with Rep. Paul Ryan (R-Wis.), chairman of the House Ways and Means Committee, to find funding for a long-term bill, but thus far, Republicans have not produced one. In the Senate, committee action on a six-year bill is scheduled for next month.

At the state and local levels, the issue is one of filling potholes, paving roads, replacing bridges and repairing transit systems. On Capitol Hill, the matter quickly becomes more complicated.

There is no consensus on how to raise the approximately $50 billion that the federal government sends to localities to fund transportation. The venerable Highway Trust Fund isn’t taking enough in from the federal gas tax these days to cover those costs.

The White House and many members of Congress have linked paying those bills to a sweeping reform of corporate taxation — legislation that won’t go anywhere before the extension expires at the end of July and that may not see the light of day this year.

“We’re not going to get a tax-reform bill done by July,” DeFazio said. “I heard Paul Ryan say he was not going to do tax reform this year.”

Cynics — and there are many of them after 33 extensions — are betting that Congress will need to pass another extension in July, this one lasting until the end of the year.

Shuster acknowledged Tuesday that another extension may be necessary to allow Ryan time to win approval for corporate tax reform. If that happens, the problem becomes even more complicated.

Unlike the just-approved extension, for which there is money in the trust fund, extending funding through December would require that Congress transfer billions of dollars from the general tax revenue fund.

Transportation Secretary Anthony Foxx likened the tricks that Congress has used to extend funding — including something called “pension smoothing” most recently — to finding money under a mattress.

“We’re running out of mattresses, we’re running out of duct tape, we’re running out of chewing gum,” Foxx said Tuesday.

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

The administration’s bill would raise annual funding by almost $25 billion. The biggest increase would come in transit funding, a 79 percent jump over current spending that would be invested in maintenance and improvements to existing systems, and in expansion of light-rail, streetcar and rapid-bus systems.

The White House bill also would increase highway spending by about 29 percent over current levels, with an emphasis on repairing deteriorating roads and bridges before investing in new construction. Some of the additional funding would go to federal regulators that police automotive, truck and bus safety.