Sure, minutes.
Assuming the recipient is snoozing in the chair in the telegraph office at the time the message is transmitted.
Otherwise you have to wait for them to make their rounds for the day.
If you're off campaigning 3 counties over, it'll be waiting when you get back (which could be weeks of continuous campaigning down the home stretch).
Days to travel? Yeah you have no conception of life at the time.
Days to prepare and make ready for that kind of trip.
Cure trail meats, pack in salt, get currency from the bank, inspect the animals to assure they are healthy enough to bear you, take it generally easy a few days to prepare yourself, contact neighbors to look after wife & kids, etc.
Because there aren't whistle stops in every cow pasture. Even at a major town, they may only see a couple of passenger trains a week.
Winter travel could have you immobilized for days.
Just let this sad claim die like it deserves.