How to reply when she says she'd like to but you're buried in a big project

When she says she'd like that, that's the signal. The question is whether she's still in it, and a lot of people in her position will say something like this and then quietly wait to see how you handle the next few days. She isn't testing whether you're a good person. She's checking whether you still want to see her or whether she's an option you've parked.

Look at what you actually told her. You gave her a reason, a time frame, and a sign that you're interested. That's more than most people get. If she replies warmly, asks a follow-up, or suggests something low-effort she can do without you, that's interest. If she goes flat and short, it may be that she was already lukewarm and your schedule just gave her an easy exit. You can't fix that with more words. You can only make your side of it clear and let her decide.

A good reply names a window and then stops. Something like the end of the month, or once a specific deadline clears. That gives her a shape to hold on to. Without it she can't tell whether you mean three days or three months, and vagueness is where people start assuming the worst.

Also keep the plan itself loose. Don't promise a specific dinner on a specific night you can't guarantee. You can say you want to meet once things calm down and suggest a rough day, while being honest that you might need to adjust. That's easier for her to plan around than a commitment you'll have to break.

Once you've replied, the next move is a check-in, not a flood of messages. If the project has you buried, one short message a few days later is enough: a question, a link she'd like, a line about something she mentioned. Keep it light and don't ask her to do anything with it. It tells her you haven't forgotten her without making her respond to your workload.

If a week or two goes by with no reply from her and no sign she's still engaged, don't chase harder. Send one honest closing line that acknowledges the timing didn't work and leaves the door open without begging. If she doesn't answer that, you've learned what you needed to. Stop there and let it go.