What to actually say
Open with this, more or less word for word: Before I say yes to this, I need us to look at what's already on my plate.
I can take this on, but something else has to move — which of these would you rather I slow down on?
It refuses nothing, it just makes the boss do the choosing they've been avoiding.
I've said yes to the last six things without flagging it, so the list is longer than it looks from your side.
Gives them information they genuinely may not have, without accusing them of not noticing on purpose.
I'm not saying no, I'm saying I need you to choose the order.
Reframes the ask as sequencing, which is much harder for a manager to argue against than a flat refusal.
If everything's a priority, I need that in writing so I'm not the one deciding what slips.
Puts the risk of an unrealistic workload back where it belongs instead of quietly on you.
How it usually goes
A version of the conversation with the push-back left in, because that is the part you need to have already heard once.
What not to say
I'm really swamped right now.
It's a complaint with no ask attached, so the boss can nod sympathetically and nothing moves.
I can't take on anything else.
Reads as a flat refusal, which invites the boss to argue about whether that's even true instead of discussing trade-offs.
You keep piling stuff on me.
Makes it about the boss's intent, so the conversation becomes a defense of character instead of a look at the workload.
If they refuse to name anything that can wait
Some managers will not choose, because choosing means owning the overload out loud. Don't wait for permission that isn't coming. Say: 'Then I'll treat the newest item as lowest priority until you tell me otherwise, and I'll send an email today confirming that so we're working off the same list.' This isn't a threat, it's a paper trail. It protects you either way — if they correct it, you get real prioritization; if they don't, you have a dated record of what you flagged before anything slipped.