Seems like this thread got way off track since the original question was about the US (union) losing not what the CSA would do or become. Ill give a brief overview for CSA before hitting the USA points. I guess the question for me first is when do they win? That could change things some. I'm going to go with Lincoln losing in '64 to McClellan.
So Lincoln loses and McClellan decides to offer peace to end the war, however by the time he is inaugurated the South is pretty much beaten so his terms are pretty much simple. The US will allow the 11 states (not the ones claimed with split governments like Kentucky or Missouri) but the South must recognize West Virginia as a state in the Union. The CSA would also have to recognize that any slave that makes it to the Union will be granted freedom and will not be returned and that any US citizen of color visiting the south for some reason must have their rights respected. Something along these lines is offered and agreed to but hey, from the southern viewpoint they are independent.
First some draw backs for the south. If i'm not mistaken the vast majority of coal and iron deposits are outside of the CSA, especially with Kentucky and WV in the Union. Birmingham was formed post war in OTL and I imagine someone will eventually form steel mills there again like the Sloss Furnaces so they will have some domestic production of steel but will have to import coal once they reach a certain threshold of industrialization but for the time being, I believe the reserves within AL, TN, small part of SW VA, and parts of TX should suffice. However, the economy will largely remain plantation/agrarian based, though eventually much like Asia took on textile plants away from OTL US, the CSA would eventually do this with cheaper labor. The problem will be the US had tremendous immigration OTL, the south will not see nearly as much due to slavery and there simply not being the need for the cheap labor initially that immigrants provide. I imagine the South resembling a third world country up until oil becomes king and the oil revenue from Texas will help it boom like the third world nations of OTL like the mid-east that grew wealthy from oil money, though it would have to diversify at some point due to smaller reserves compared to mid-east. One point of the south OTL, post war and really even to this day, most of the South have received more federal tax distributions than they give to the government, meaning you wont have that income for them to live off of so they will have to develop. Best bet for a productive, powerful CSA would be at earliest mid 20th century, though I think '70s or'80s is more likely.
Now as for the US. Having given up the CSA states they still have the rest of the territory they held and coast to coast access. They still finish the trans-continental railroad started under Lincoln and most likely still make a push to buy Rupert's land and Alaska. Most likely, just like OTL, the UK steps in to stop the Ruperts Land sale but Alaska still happens. You may, however, see a larger focus of US citizens going into BC so there is a greater chance the US could end up annexing it at some point. Not a sure thing by any means but more possible in new TL. Also, the US didn't suffer near the damage on it's own soil during the war as the south would have had by March of 1865, so the money the US spent rebuilding the south now gets spent on debt payments and other capital projects or even buying more land like Alaska. Seward proposed the idea of buying Greenland and Iceland from Denmark in 1867 but no official offer was made IIRC. So you might see a stronger push to make that happen.
Lets just assume Alaska and Hawaii get added as well as other OTL Pacific holdings. Lets look at demographics first. The vast majority of blacks ( Dont know exact amount but something like 85 to 90% maybe a little more) were in the south. After the civil war, this mostly remained unchanged until the great migration in early 20th century, leading blacks to migrate north and provide good cheap labor that immigrants from Ireland and other European countries had provided. You wont get this in OTL as there would be immigration quotas at some point though some surely will make there way across. One must also wonder if race relations improve more in the Union than OTL. For example, would a smaller black population lead to less conflict and maybe more acceptance that you tend to see in modern UK? Relations are by no means perfect there but I could easily make the argument that blacks are treated better in modern UK than they are in the US, especially southern US OTL. So while there would still be blowback, just like OTL against Irish / Catholics, you probably don't see the same level which means more stability. More stability means greater economic growth. I would not be surprised if the CSA eventually got hit by it's own civil war once blacks were freed or maybe even a large scale slave rebellion, you might even see a 2nd war with the Union as they offer to help the rebels.
Economic growth being the next point, The US had a clear overall population edge in OTL and would retain that. It wasnt really until AC was invented that you started seeing a real shift south towards cheaper land and production. This allows the US to still establish a dominant manufacturing and textile industry and the major ship building areas are still in the US as well compared to the CS. All the major manufacturing centers in the Union during the war would remain so post war so they would already have the edge there. While there are certainly resources in the south, everything the US needs to be successful is in its territories, even most of the Uranium mining is in US hands. I think TX has some deposits but nowhere else in the South going by a quick google search. The only draw back will be the loss of TX oil though I'm sure the US will still import plenty and probably cheaper than abroad simply due to it's location close to TX, though you still have oil in PA, OK, and AK. You also have key trade ports in NYC, Philly, LA, Seattle, all within the US.
Let me say this as someone with deep southern roots. Having a united country with the South definitely helps from a defense perspective and certain resources like timber. However, in trying to be objective I feel 100% confident in saying the US would in no way be hindered in becoming a global power without the CSA attached. I think the only real difference is you may see a larger regular army and navy with a potential hostile nation in the CSA. I'm really fascinated to see how the US would respond to Cuba. Many people automatically assume the south making a play for Cuba but they would be so battered in this TL economically and with loss of generation of men that I can't see them realistically buying or taking any territory for several decades at minimum. So does that mean no Spanish-American war or just one with the Union? The Teller amendment came about to protect US sugar industry not out of some altruistic gesture to protect Cuba. Without the Southern sugar industry, maybe there is a war but no amendment and the US ends up with Cuba, thus stopping CSA expansion. Plus there may not be the same hesitancy to add a large black population that Cuba had in this new TL. Regardless of how expansion goes, I repeat my statement. The US could and would have been able to achieve superpower status without the South. I know their are other things I'm not thinking of off the top of my head but I truly believe anyone arguing against the idea could be successful refuted.