I'm swamped at the moment.

Meaning

I'm very busy right now.

Examples

• John: Can you help me with this?
• Alice: Sorry, <b>I'm swamped at the moment</b>. I'll try to get to it later.
• John: Okay, no problem. Let me know when you have some free time.
• Alice: Thanks for understanding. I really am <b>swamped at the moment</b>.