WASHINGTON – What happens if President Obama and Congress don’t strike a debt deal?

On Aug. 3, the nation would find out, with Obama forced to make a set of extraordinarily difficult choices about what to pay or not pay. By then, the government’s savings account would be nearly empty and the president would be relying on daily tax revenues to pay the nation’s bills.

There wouldn’t be enough — in fact, there would be a $134 billion shortfall.

As Obama decided what to pay, he would choose among Social Security checks, salaries for members of the military and veterans, unemployment benefits, student loans and many other government programs, according to administration officials and an independent analysis by a former senior Treasury Department official in the George H.W. Bush administration.

To protect the nation’s creditworthiness, Obama would have to balance those priorities with the imperative of making payments to investors in U.S. government bonds — which range from domestic pension funds to the Chinese government.

“You can move the chess pieces around all you want,” said Jay Powell, a visiting scholar at the Bipartisan Policy Center and the author of the analysis. “You’re going to lose.”

For months, the president has been pressing Congress to raise the federal limit on borrowing, now at $14.3 trillion. Members of both parties have balked, saying they first want a plan to tame the growth of the debt.

On Wednesday, with negotiations over raising the debt ceiling hung up, Moody’s said it might downgrade the U.S. government’s top-of-the-line credit rating, which helps keep U.S. bonds the global gold standard, “given the rising possibility that the statutory debt limit will not be raised on a timely basis, leading to a default.”

Obama says he must reach an agreement by July 22 to get legislation through Congress and meet an Aug. 2 deadline, after which the Treasury Department projects it will no longer have enough money to pay for all U.S. obligations. Treasury Secretary Timothy Geithner has warned that a default would deal a severe blow to the economy.

Some economists and skeptics in Congress say that Obama has overstated the risk of not raising the debt ceiling and that tax revenues could pay for up to 60 percent of government operations.

“You do not have to default and you don’t have to shut down the government if you chose not to,” said Peter Morici, an economist at the University of Maryland. If Congress raises the debt ceiling without a long-term plan for reducing the federal deficit, he added, “They’ll never solve the problem, and we’ll end up like Greece.”

On Wednesday night, several Republican leaders were briefed on the contents of the Bipartisan Policy Center report as concern grew in the party about the potential impact of not raising the debt ceiling.

According to the center, the government would have to cut 44 percent of spending immediately. Through August, it could afford Social Security, Medicare and Medicaid, defense contracts, unemployment insurance and payments to bondholders.

But then it would have to eliminate all other federal spending, including pay for veterans, members of the armed services and civil servants, as well as Pell grants, special-education programs, the federal courts, law enforcement, national nuclear programs and housing assistance.