Pushing back on a shift you cannot work when refusing has a cost
Refusing an assigned shift is never free. You can make it cheap. The text, the short-notice version, and the three honest options when the answer is no.

Most advice on this pretends there is a way to decline a shift that costs nothing. There usually is not. A scheduler who has to solve your problem at short notice remembers it, and that memory gets paid back later in ways nobody announces.
You cannot make that cost zero. You can make it much smaller, and what does it is not your reason. It is whether you arrive with the hole already filled.
What refusing actually costs
Be honest about the size of it, because that should change how you spend your goodwill.
- Fewer hours. In most hourly work the scheduler decides how many hours you get, not a contract. The usual penalty, and rarely announced.
- Worse shifts. Split shifts, clopens, the Sunday nights.
- Being asked last, which matters if you want overtime hours.
- Formal discipline. Real in some workplaces, especially where there is an attendance points system. If yours has one, find out what a refused shift costs in points before you refuse.
Use your two or three a year on the shifts that actually matter and work the rest.
Fill the hole first
Fifteen minutes of work before you send anything changes the conversation. Go to the group chat or the swap board and find a specific person who will take it. Not "someone will probably pick it up." A name, and a confirmation you can point to. Ask people who want hours, not people who owe you favors. On any shift team two or three are chasing hours, and they say yes fast.
The text, written out
Short, and sent through the scheduling app or by text rather than said in a hallway. Managers of hourly teams read on their feet, and long messages get skimmed.
"Hi [supervisor] - I can't work Saturday the 12th, 2 to 10. I've asked around and [a coworker] says he'll take it, he's messaged you separately to confirm. Anything you need from me to get it swapped? Sorry for the hassle."
Four parts, in order. The shift named precisely so nobody has to look it up. The problem in five words. The solution, with a name. An offer to do the paperwork yourself.
No reason is given, and that is intentional. A reason turns the exchange into a judgment about whether it is good enough, and it sets up the next request to be measured against this one. If your manager asks, answer in one sentence and stop.
When it is short notice
A different message, because now you are asking rather than solving.
"[Supervisor], I'm sorry, this is short notice. I can't make the 6am tomorrow. I've tried three people on the schedule and nobody can swap. I can do Sunday or Monday instead if that helps. I know this is a hard one to fill and I wouldn't ask if there was another way."
Three differences. You apologize once, properly. You show the work you did, by name, so it is clear this is not a first resort. And you offer something concrete back.
Never leave it ambiguous
"I don't think I can do Saturday" reads as a complaint rather than an absence, and the shift stays on the grid with your name on it. If you are not coming, say so as a statement. If nobody has answered by the swap cutoff, say it again plainly. Most attendance penalties come from a shift everyone assumed was handled.
When the answer is no
Sometimes it is no. Three honest options, no trick.
Work it. Not a defeat. If refusing is expensive where you work and the reason you wanted off is movable, move it and you have spent nothing.
Escalate once. "Is there anyone else who can approve a swap if someone else is willing to take it?" Some schedulers say no because approving a swap is work, not because coverage is a problem. One question finds out which you have.
Decline anyway, knowing the price. Say it plainly, once, and do not argue: "I understand, but I'm not able to be there Saturday. I've told you as early as I can and I've found someone willing to cover." Then accept what follows without relitigating it.
The people who hold the line successfully are the ones who almost never need to. Say yes often enough that your no means something.
If you are sick, or it is not really a choice
Illness, a child with nowhere to go, a car that will not start on a route with no bus. These are not negotiations, and dressing them up as one weakens you.
Say it once and flatly: "I'm sick and I can't come in today. I'm following the call-out process and I'll send anything you need." Then follow that procedure exactly, including the timing and the person to call. Most attendance penalties come from a missed step, not from the absence.
Where the rules vary
This is US-specific and varies a great deal below the federal level. Several cities and a handful of states have predictive or fair workweek scheduling laws, which can require advance notice of schedules, premium pay for late changes, and sometimes the right to decline a shift added at short notice without penalty. Coverage is usually limited to retail, food service and hospitality, and the details differ wherever they exist.
Paid sick leave is also state and city law in much of the country and nonexistent in the rest. Do not assume either way. Your state labor department, and your city's if it has one, publish plain-language summaries of what applies where you work. Check there before concluding you have none.
General information about work in the United States, not legal, tax, immigration, medical or financial advice. Pay, hours, leave and licensing rules differ by state, by city and by contract, and change over time. Check anything here against your own documents and, for anything you would act on, take advice from a qualified professional in your state. Get in touch with any questions about this post.