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 revenue to pay the nation’s bills.

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

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 — ranging 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 an 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 F. Geithner has warned that a default would deal a severe blow to the economy.

Some skeptics in Congress and conservative economists say that Obama has overstated the risk of not raising the debt ceiling and that tax revenue 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 choose 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.”

Obama’s advisers have said that prioritizing some payments over others is impractical and would be chaotic. Money comes in and flows out at an inconsistent rate.

“You would have to make heinous choices about which bills you would pay,” White House press secretary Jay Carney said Wednesday.

On Wednesday night, several Republican leaders were briefed on 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’s analysis, the government would have to cut 44 percent of spending immediately. Through August, the government could afford Social Security, Medicare, 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 funding for Pell grants, special-education programs, the federal courts, law enforcement, national nuclear programs and housing assistance.

After the debt ceiling was breached, there would be no delay in the tough decisions.

On Aug. 3, the Treasury is set to receive about $12 billion in tax revenue — mainly from people paying their taxes late — and is slated to spend $32 billion, including sending out more than 25 million Social Security and disability checks at a cost of $23 billion, according to Powell’s analysis.

Obama could decide to pay half of the Social Security checks and ignore other bills coming due that day, which include $500 million in federal salaries and $1.4 billion in payments to defense contractors.

Or he could decide not to make any Social Security payments and instead hoard tax revenues to pay investors in U.S. bonds. A failure to pay those investors would severely destabilize the financial system, analysts say. (Some also argue that the Treasury could engage in a never-before-tried swap of government bonds that would allow it to pay for Social Security. But Treasury officials say it is highly unlikely to work and may not be legal.)

Aug. 4 could prove even more difficult. The government is slated to spend $10 billion and raise only $4 billion in revenue.

More worrisome for government officials is the $100 billion in Treasury bonds that come due on Aug. 4 and must be paid off. Ordinarily, Treasury would pay off those bonds and issue new bonds.

But if the debt ceiling isn’t increased, Treasury could run into trouble “rolling over” this debt. Ratings agencies are threatening to downgrade U.S. bonds if the debt ceiling isn’t raised. If the bonds are downgraded, many investors — such as retirement funds — can’t buy them.

As a result, there could be far fewer buyers of Treasury bonds and the U.S. government would have to pay much higher interest rates.

Government officials and analysts say a spike in rates would dramatically increase the cost of funding the government and lead to far higher interest rates on mortgages, credit cards and other types of debt.