This is such a silly argument. Lincoln managed to run the government quite effectively for four years without southern revenue, and at a hugely greater level of expense. By mid-1863 the Union was spending about as much each month as it had spent in all of 1860. By the end of the War it had spent around $6B, or roughly 100 year's expenditures at the 1860 level.
The Union's economy performed at gang-buster levels during the War. Industry grew at massive speed. Agriculture throve, with exports booming.
Tell us again why the Union would collapse without southern revenues.
The North suffered a balance of payments problem without exports of Southern cotton. Inflation and debt was the result.
... exports booming.
Not enough to make up for what they were importing. Let's look at 1863. From Appletons Annual Cyclopedia for 1863, page 190:
... the foreign commerce of the country had greatly contracted in face of improved harvest in Europe. ... The "balance of trade," so called, may then be approximated as follows: ... Excess Imports [rb note: imports over exports]: $74,295,706. Net specie export, direct: $54,689,903 [rb note: It's hard to read some of the last six digits on my copy. The North's exports were mainly food stuffs (and petroleum surprisingly) to Europe.]
In constant 1860 dollars, imports were way down during the war compared to 1860.