Probably closer to a few hours across the Atlantic. Recall the early trans-oceanic cables suffered from weak signal strength so a message would have to be transcribed, transmitted, receipt acknowledged and likely transmitted and acknowledged several times again so the final transcription at the receiving end was as error free as possible. Still an order of magnitude gain in speed of communications.
There where no (working) trans-oceanic cable during the 1861-1865 period.
The first one was in operation before the war, but it broke and not until 1866 was there a new one in operation.
My point is that communication within the north american network was very very quick. (compared to a guy on a horse... or later a train)
The moment you left the network it could easy be days until you go the message.
Obviously having this quick connection between army and the political leadership also gave the generals less freedom to do as they thought best, since it allowed the Guys in the capital to interfere more.
In February 1864 at the start of the 2nd Sleswig war, the leadership of the danish field army decided to pull back from the fortified Dannevirke line. They telegraphed this decision to Copenhagen, then quickly cut the line before the Politicians could countermand them.
Since pulling back was the correct decision militarily, but a political disaster. That is One way of getting around this issue.
(but the decision o pull back did cost the commanding general his post)