I was checking on Western Alienation online and the result I got is that it is part of Canadian politics with various provinces deciding whether to secede or not. From what I understand, the US would have the same thing but it is going to be much more volatile given the increasing sentiment following the war, but wouldn't such sentiment for a Pacific Republic wax and wane over the years?
I am not sure if the Western US becomes independent or whether different national boundaries in North America equates to more nations appearing in North America, but given how this timeline has gone, I wouldn't be surprised if a Pacific Republic appears in the 20th century (Western alienation being a huge US political issue in the latter half of the 19th century suggests a Pacific Republic won't happen 50 years down the line) like the US losing another massive war down the line. But with the need to rebuild the US, it is likely the east would be prioritized over the west, further souring relations. If the west managed to rebuild without support from the east, it could embolden the independence movement in California, Oregon, and Washington state.
Personally, I don't think Washington would allow an independent Pacific Republic after the Confederacy broke off, and it would further tarnish their international standing while empowering their enemies. I am not sure how the US would deal with this but it might relate to the different national borders. For all I know, a war of secession breaks out in the West and the US manages to defeat it to prevent another potentially hostile front and that is how General William Lincoln's career begins ITTL. And it would be even crazier if the sentiment for a Pacific Republic spread to Western Canada because they feel left out of the Kingdom of Canada and form an independent Republic of Cascadia with Alaska in it, but what are the odds of that happening?
But whatever happens later, I'm sure you will make it interesting.
Like the Canadian political term I based that off of, the desire for independence on the Pacific slope will indeed wax and wane over the years, its currently fermenting just under the surface, since the anger is primarily at Lincoln and his administration for how California and the other states/territories were left out to dry and got invaded by Britain - as well as some savage little Indian wars they have to deal with on their own - as well as having greenbacks imposed upon them.
In the medium term much will depend on how well McClellan's administration handles the economy. Part of that is managing the ballooning national debt, but also managing how the resources of California are taken care of. Railroad politics and the desire for a Pacific Republic are going to be huge bedfellows. However, down the line the knowledge that being displeased with Washington means you can secede will of course be a factor in the thinking of these states. I have a few actors of the movement in mind, and I'm hoping it will seem interesting as the tumultuous decades keep on rolling! The 1868 election is going to cause some contention I can assure you.
Canada's own trek to the Pacific is going to be interesting in some familiar and unfamiliar ways. In 1865 alone British Columbia and Vancouver colonies are going to have a rough year, but when Canada comes knocking they will still be desirous to sign up as Macdonald still has a deft touch in politics. The work of getting across the continent however, will be much more demanding.