WASHINGTON (AP) — The Senate voted Tuesday to give a tax break to new car buyers, setting aside bipartisan concerns over the size of an economic stimulus bill with a price tag approaching $900 billion.

The 71-26 vote came as President Barack Obama said he lies awake nights worrying about the economy, and signaled opposition to congressional attempts to insert ‘‘buy American’’ provisions into the legislation for fear it would spark a trade war.

Sen. Barbara Mikulski led the successful effort to allow many car buyers to claim an income tax deduction for sales taxes paid on new autos and interest payments on car loans.

She said the plan would aid the beleaguered automobile industry as well as create jobs at a time the economy is losing them at a rapid rate. ‘‘I believe we can help by getting the consumer into the showroom,’’ she said.

The provision was attached to the economic stimulus bill at the heart of Obama’s economic recovery plan and is subject to change or even elimination as the measure makes its way toward final passage.

Democratic leaders have pledged to have the bill ready for his signature by mid-month, and in a round of network television interviews, the president underscored the urgency. He told CNN that even three months ago, most economists would not have predicted the economy was ‘‘in as bad of a situation as we are in right now.’’

He also spoke out against efforts to require the use of domestic steel in construction projects envisioned in the bill, telling Fox News, ‘‘we can’t send a protectionist message.’’

The stimulus bill remains a work in progress, following last week’s party-line vote in the House and an Oval Office meeting on Monday in which Obama and Democratic leaders discussed ways to reach across party lines.

In a series of skirmishes during the day, the Senate turned back a proposal to add $25 billion for public works projects and voted to remove a tax break for movie producers. Both moves were engineered by Republicans who are critical of the bill’s size and voice skepticism of its ability to create jobs.

Democratic leaders conceded they may soon be obliged to cut billions of dollars from the measure. ‘‘It goes without saying if it’s going to pass in the Senate, it has to be bipartisan,’’ said Sen. Dick Durbin of Illinois, the second-ranking Democratic leader, adding that rank-and-file lawmakers in both parties want the bill’s cost reduced.

One Democrat, Sen. Ben Nelson of Nebraska, said he hoped for reductions ‘‘in the tens of billions of dollars.’’

The developments unfolded as more companies announced job layoffs — including 5,800 at PNC Financial Services Group. In another sign of economic weakness, the Federal Deposit Insurance Corporation predicted the cost of bank failures will exceed its estimate from last fall and urged lawmakers to more than triple the agency’s line of credit with the Treasury Department to $100 billion from the current $30 billion.

Mikulski’s office put the cost of the tax break she sponsored at $11 billion over 10 years. It would apply to the first $49,500 in the price of a new car purchased between last Nov. 12 and Dec. 31, 2009. Individuals with incomes of up to $125,000 and couples earnings as much as $250,000 could qualify, including those who do not itemize their deductions. A couple would save an estimated $1,553 on a new $25,000 car, aides said.

Sen. Charles Grassley, R-Iowa, sought unsuccessfully to derail the proposal, saying it would only increase consumer debt in a time of recession and adding that there were other provisions in the legislation to help the auto industry. But the 71 votes in support were far more than the 60 needed for passage.

Earlier, the vote to add $25 billion for new construction on highways, mass transit and water treatment facilities failed 58-38, two short of the 60-vote majority needed for passage.

Sens. Dianne Feinstein, D-Calif., and Patty Murray, D-Wash., argued the increase would quickly translate into jobs.

‘‘Our highways are jammed. People go to work in gridlock,’’ Feinstein said in arguing for the proposal.

But Sen. Jim Inhofe, R-Okla., countered, ‘‘We can’t add to the size of this bill. … The amount is just inconceivable to most people.’’

Sen. Tom Coburn led the successful effort to remove a provision allowing movie makers to write off their expenses more quickly. The vote was 52-45, despite protests from Sen. Max Baucus, D-Mont. He said Hollywood was the only industry denied the break in a tax bill two years ago.

Republicans are expected to seek a vote later in the week on a plan to inject the government into the mortgage industry in an attempt to drive down the cost of mortgages to as low as 4 percent. Democrats treaded carefully on the proposal, saying they would consider it but also claiming the $300 billion Republicans allocated would not come close to accommodating the demand.