I'd say: Not that much. Cotton was already the third cash crop plantations had switched to after sugar, rice and on occasion indigo and tobacco. In the longer terms the plantation system would survive by switching to the next cash crop or moving out to areas that were not effected by the blight. OTL, many Carolina plantation owners settled in Texas after a string of bo-weevil infestations killed their crops back home. It was thought that the dryer climate of West Texas was unsuited for weevils. Something similar could happen on a bigger scale in the 1850's. If this would happen before the annexation of California, prepare many plantation politicians demand that California be a slave state so they could set up shop.over there and cultivate fruits and beans. In any case, most plantation owners that have some savings put up, will go back to rice or tobacco for a couple of years while figuring out the next big crop or trying to find a blight-resistant variety of cotton. (OTL, many plantation owners of South Carolina also had a second income from mining nitrates from local lodes on their properties, so this could help too.
In the short term however we might see three years of economic crisis played out as many of the smaller or less prosperous plantations will have to sell off a good deal of their slaves to pay their bills. This might lead to the prices for slaves collapsing and as some plantations will still struggle paying back loans, this will eventually effect the markets in the North. So expect a rising anti-southern anti-slavery sentiment in the northern states but with the South just doubling down on their old ways. This will split the country even further and by 1860 it will be a given that civil war will occur sooner or layer.
Perhaps the Civil War, when it will inevitably occur will be a couple of months shorter because of the South being out of resources earlier, but don't expect the war to happen in 1857 already.