Debunking the lie not raising the debt ceiling will cause the US to default on debt

Here is the big lie from the Liar-in-Chief:

Via The Hill:

President Obama said Republicans in Congress were threatening to make the United States into “a deadbeat” and a “banana republic” with their maneuvers to tie the federal budget and the debt ceiling to defunding ObamaCare.

Here is the 2013 federal budget and revenue for the fiscal year that ends October 1, 2013.

Via Wikipedia:

Total revenues and spending

The Obama administration's February 2012 budget request contained $2.902 trillion in receipts and $3.803 trillion in outlays, for a deficit of $901 billion.^[38] The budget projects a reduction in the deficit to $575 billion by 2018 before rising to $704 billion by 2022.^[39]
Total receipts (in billions of dollars)::

Item	Requested[38]
Individual income tax	1,359
Social Security and other payroll tax	959
Corporate income tax	348
Excise tax	88
Customs duties	33
Estate and gift taxes	13
Deposits of earnings and Federal Reserve System	80
Other miscellaneous receipts	21
Total	2902

Total outlays by agency (in billions of dollars):

Agency	Discretionary	Mandatory	Total
Department of Defense including Overseas Contingency Operations	666.2	6.7	672.9
Department of Health and Human Services including Medicare and Medicaid	80.6	860.3	940.9
Department of Education	67.7	4.2	71.9
Department of Veterans Affairs	60.4	79.4	139.7
Department of Housing and Urban Development	41.1	5.2	46.3
Department of State and Other International Programs	56.1	3.4	59.5
Department of Homeland Security	54.9	0.5	55.4
Department of Energy	35.6	–0.6	35.0
Department of Justice	23.9	12.7	36.5
Department of Agriculture	26.8	127.7	154.5
National Aeronautics and Space Administration	17.8	–0.02	17.8
National Intelligence Program	52.6	0	52.6
Department of Transportation	24.0	74.5	98.5
Department of the Treasury	14.1	96.2	110.3
Department of the Interior	12.3	1.2	13.5
Department of Labor	13.2	88.4	101.7
Social Security Administration	11.7	871.0	882.7
Department of Commerce	9.5	–0.5	9.0
Army Corps of Engineers Civil Works	8.2	–0.007	8.2
Environmental Protection Agency	9.2	–0.2	8.9
National Science Foundation	7.4	0.2	7.5
Small Business Administration	1.4	–0.006	1.4
Corporation for National and Community Service	1.1	0.007	1.1
Net interest	246	0	246
Disaster costs	2	0	2
Other spending	34.0-	61.7	29.5
Total	1,510	2,293	3,803

Revenue in the 2013 budget is $2.9 trillion and spending is $3.8 trillion. That means we borrow $900 billion. That's where the debt ceiling comes into play. We can see mandatory spending is $2.3 trillion. Add back in the rest of the military spending, except $140 billlion for new procurement, the payment of $246 billion on the national debt interest and we have a grand total of 3.07 trillion in spending.  Since revenue was 2.902 trillion, we only have to come up with $160 million. The actual budget was different than the on passed by Congress and signed by Obama. Due to the sequestration and increased tax revenue, the CBO estimates the actual deficit at $759 billion. That is a savings of $161 billion. This covers the $160 billion gap. Without raising the debt ceiling, we have paid all mandatory federal spending, paid all the defense budget, except for delaying new procurement, and paid the interest on the national debt. Now tell me how not raising the debt ceiling will cause the US to default on it's debts?