Of course it would take months. So what? Is the CSA going somewhere? Nitrates aren't gold or platinum. It is pretty common stuff. GB was merely a cheaper source.
In fact any future setbacks can then be blamed on the interfering Brits. The problem is that is more likely to make people more stubborn as outsiders are interfering in their affairs.
Sorry, are you saying that the Union would prosecute any war no matter how hard it was? That no consequence on Earth would possibly result in the Union giving up, or even agreeing to negotiate?
If the economy was in the toilet to the same extent as OTL War of 1812, say?
Anyway - Nitrates.
They're not gold or platinum, no. They're more like oil, or iron ore - they can be sourced from many places but at this time OTL the British could outproduce anyone else on volume. The Union is simply unable to produce the same amount of nitrates as they could source from the UK, not when OTL they were expanding production PDQ as it was to
reduce that foreign dependence and they were still sourcing from the Brits.
Add on the demands of, say, another theatre of war to the north... it all adds up.
And in terms of many extra months on the war...
The thing most likely to lead to an ultimate CSA survival would be that the war is not clearly close to a victory during the 1864 election.
If the election happens not long after some major Confederate high water mark-type event, with CSA forces still able to operate in Pennsylvania or Maryland (which requires an extension of not much more than a year, quite doable with the Nitrate problem among a few other pressures or even French regulars fighting alongside the CSA) then it will look like a long, grinding, pointless war.
At that point it's "more of this or a peace with honour".