Given that the only way the Federals are doing such things is either a) something like firing on the batteries around Sumter, or b) with troops that have volunteers - the Regular Army is in no position to do anything on its own except something like the Sumter scenario - I'd say "Almost not at all".
The "conditional Union" states left simply at the idea of volunteers called up to fight when the US had been attacked, so they're hardly going to be more hostile than OTL. The Border states aren't particularly sympathetic to the Confederacy, and foreign powers . . . aren't going to care.
The reason I ask is that Fort Sumter was, forgive the comparison, akin to a Pearl Harbor, with the American people rallying to the war effort, in this case patriotic fervor seizing many in the North, and to some extent in the Border States.
Without this fervor as we saw it, the response to Lincoln's call for volunteers (which will come at some point) will be far from enthusiastic.
The most significant change I can see is the secession of Maryland, oddly the closest of the four border states; there would be less Federal sympathy in the area, and Governor Thomas Hicks, remaining ever more mixed on the opinion of the Federal Government, would have proceeded to call a Convention in Annapolis, resulting in the passage of Secession (so a POD creating a line of PODs).
Kentucky, I imagine, could also maintain some manner of neutrality given loses in the elections held in '61, which had produced in OTL veto-proof Unionist chambers, would be more mixed (given more people would be willing to vote for Southern sympathizers, and those Southern sympathizers that did exist would actually turn out to vote), though likely still leaning in the favor of the Unionists. Therefore the Governor, Beriah Magoffin, could continue his course of indirectly supporting the South, while maintaining for pragmatic reasons the neutrality of his state.
Missouri I imagine would be the same until the Price-Harney Truce, where things begin to diverge. This could be argued, but I could see Lincoln deciding to ignore the anger directed to him by the Unionists from Missouri, principally Francis Blair, and keeping Harney in command; being on the fence, he would decide against it so as not to already aggravate a delicate situation (Kentucky already standing on the line, Maryland having officially seceded), while still being in position to move into the remainder of the state from St. Louis (the one place Federal troops were allowed) should Missouri not abide. However, given it requires respecting Missouri's neutrality (in return for its promise to remain in the Union), this cuts off the Western Theater as we know it.
Just some stuff to think about.
Without this fervor as we saw it, the response to Lincoln's call for volunteers (which will come at some point) will be far from enthusiastic.
The most significant change I can see is the secession of Maryland, oddly the closest of the four border states; there would be less Federal sympathy in the area, and Governor Thomas Hicks, remaining ever more mixed on the opinion of the Federal Government, would have proceeded to call a Convention in Annapolis, resulting in the passage of Secession (so a POD creating a line of PODs).
Kentucky, I imagine, could also maintain some manner of neutrality given loses in the elections held in '61, which had produced in OTL veto-proof Unionist chambers, would be more mixed (given more people would be willing to vote for Southern sympathizers, and those Southern sympathizers that did exist would actually turn out to vote), though likely still leaning in the favor of the Unionists. Therefore the Governor, Beriah Magoffin, could continue his course of indirectly supporting the South, while maintaining for pragmatic reasons the neutrality of his state.
Missouri I imagine would be the same until the Price-Harney Truce, where things begin to diverge. This could be argued, but I could see Lincoln deciding to ignore the anger directed to him by the Unionists from Missouri, principally Francis Blair, and keeping Harney in command; being on the fence, he would decide against it so as not to already aggravate a delicate situation (Kentucky already standing on the line, Maryland having officially seceded), while still being in position to move into the remainder of the state from St. Louis (the one place Federal troops were allowed) should Missouri not abide. However, given it requires respecting Missouri's neutrality (in return for its promise to remain in the Union), this cuts off the Western Theater as we know it.
Just some stuff to think about.