Having one's hands full; being so busy or fully occupied that one cannot take anything else on.
今週は仕事が立て込んでいて手一杯だ。
This week work is piled up and I'm completely swamped.
小さい子どもの世話で手一杯で、趣味の時間が取れない。
I'm so busy taking care of my small child that I have no time for hobbies.
新しいプロジェクトを任されて今は手一杯だ。
I've been put in charge of a new project and I'm fully occupied right now.
彼は電話対応で手一杯なので、後でかけ直す。
He's tied up answering calls, so I'll call back later.