They'll have plenty of money to pay the interest on the debt (no default) and to mail out SS checks. If it doesn't get paid, it's because they chose not to.

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Bipartisan Policy Center: U.S. Won't Default on Debt If Congress Fails to Raise Debt Ceiling
But drastic and immediate cuts would occur.

With under a month left until the U.S. hits its statutory limit to borrow more money, Republicans and Democrats continue to disagree about what exactly would happen if Congress and the president fail to reach an agreement that raises the debt ceiling.

"Failure to raise the limit would precipitate a default by the United States," wrote Treasury Secretary Timothy Geithner earlier this year. No, that's not true, say Republicans. There's enough federal revenue to pay the interest on the debt as well as fund the troops and entitlement programs.

According to a study by the Bipartisan Policy Center (BPC), Treasury could indeed avoid a debt default by prioritizing payments, but failure to raise the debt ceiling would mean deep and immediate cuts.

[excerpt]

The BPC study found that the United States is likely to hit the debt limit sometime between August 2 and August 9. “It’s a 44 percent overnight cut in federal spending” if Congress hits the debt limit, Powell said. The BPC study projects there will be $172 billion in federal revenues in August and $307 billion in authorized expenditures. That means there's enough money to pay for, say, interest on the debt ($29 billion), Social Security ($49.2 billion), Medicare and Medicaid ($50 billion), active duty troop pay ($2.9 billion), veterans affairs programs ($2.9 billion).

That leaves you with about $39 billion to fund (or not fund) the following:

Defense vendors ($31.7 billion)

IRS refunds ($3.9 billion)

Food stamps and welfare ($9.3 billion)

Unemployment insurance benefits ($12.8 billion)

Department of Education ($20.2 billion)

Housing and Urban Development ($6.7 billion)

Other spending, such as Departmens of Justice, Labor, Commerce, EPA, HHS ($73.6 billion)

[link to www.weeklystandard.com]