Food, gold, oil, coal, iron, steel, furniture, railroad engines, chemicals, machine tools, glass, toys, books, paper, wood, tin, copper, steam engines etc. etc. The US would have NO problems paying its bills. The CSA on the other hand had nothing but cotton and tobacco.
Food - yes they can sell wheat, but they can't float the whole economy on it and they are competing on the world market. Notice that the moo cows are in Texas which is part of the CSA so at best beef becomes an import that has to be paid for (to the CSA). Also note that a CSA would be more receptive of British opportunities than was OTL USA and perhaps we end up with corned beef for the British colonies comming from the CSA and not the Argentine? At worst Chicago never becomes the meat processing hub it was in OTL and that hub ends up somewhere in the CSA. Similar story (but less extreme) for hogs.
Oil - Far more of it in the CSA than the USA and demand does not really become large until the 1900s.
Gold - not if it is in California and California has left the Union
Coal - who are they going to sell it to? The best steam coal is in Wales. Metalurgical coal is everywhere. This is a domestic product only.
Iron - well iron production in the USA in the ACW was very primitive the biggest production plant was still using charcoal when the rest of the world was using coke. Who is going to invest in new plant? The best foundry in the Ante-Bellum USA is in the CSA post war.
Steel - the first Besemer converter in the USA was built 1863 and production really began to ramp up in the 1870s but in this scenario why would the British capitalists invest? Why not put the plants in the CSA where costs will be lower. The CSA will of course buy its steel rails from Britain as they will be cheaper (including transport) and better than rails from the USA.
Furniture - I don't recall it being a major European import. I do know it was tariff protected to stop the British undercutting the USA manufacturers in the domestic market. So this is not likely to make a contribution.
Railroad engines - only a domestic product. USA built engines were low efficiency compared to British and even Prussian engines. Without tariff protection the domestic manufacturers are undercut by the Europeans and the CSA will either buy European or develop a domestic product or both.
Chemicals - well all the sulphur is in the CSA. The USA will no longer be able to control a significant part of the nitrates trade (due to increased distances). So what chemicals do you think the USA will trade.
Machine tools - No. Just no. They could not compete with the British without tariff protection they won't even be able to compete domestically.
Glass - everybody makes glass - little export potential here.
Toys - miniscule market in the mid-Victorian period.
Books - can't see this making an economy work alone!
Paper - yep but more trees in Canada/BNA. Once again no tariff protection any more.
Wood - not really a export earner is it. Unless there are some really unique trees in the USA I don't know about like Kauri in NZ or mahogany?
Tin - from whence?
Copper - yes this one is the first major valid export earner.
Steam engines - This is funny, in the ACW many USA built steam engines still had hardwood cog wheels. They were decades behind the British. Who could they possibly sell a steam engine to other than domestically and even that industry would collapse without tariff protection.
The ones that I am aware of that you have missed are parafins which was becoming a big market and whale oil which was also a big market but of course in a British intervention they have probably sunk most of the whaling fleet. Small mechanical devices like type writers and similar but not a big market.
So as you can see from the above your assertion that the USA could pay its bills is almost certainly false simply because they have almost nothing to export and without tariff protection most USA manufactories cannot even compete domestically.
Notice also that for exports to fund the USA Govt the USA Govt needs to charge a customs duty or tariff on the export which would make it even more expensive compared to the European product. If they want to collect the money from domestic manufactures they need some sort of tax which will be a further pressure contracting the economy. The USA in this scenario (CSA Independence through British intervention and possible loss of California) is in really really bad economic shape.
The CSA has considerably more than cotton and tobacco as you suggest. They have oil, beef and hogs as I have discussed. They have ship building, they have coal and iron, they have sulphur, fishing and they will completely take over 2/3s of the fishing and coastal shipping trade that had once been the USA's. They can easily import textile technologies.