Learning when to bluff and when not to is an important part of negotiating. Some people thing it's a good idea to bluff all the time -- it's not and can easily backfire.
plus, you'll get reamed if you later get caught telling a lie, and ethics matter (at least for some of us).
With regards to expressing urgency, maybe something like: "I appreciate that you've got a busy schedule. Boy, can I empathize, it seems like I have to slide the actual running of the company in between the fundraising. But, you know, the market's the market right now. I'll tell you the same thing I'd tell everyone else: we'd be happy to pencil you in for X but our situation is evolving and there may not be an open window for this by X."
(I've never raised money, but when I sell consulting gigs, I typically throw in a true observation like "I have N weeks of availability. My experience is that I usually book up." Ask the 500 crew, but it seems to me like "We're a 500/YC/etc startup. Historically, the rounds sometimes close out quickly." is absolutely true, conveys urgency, leverages social proof, and doesn't say anything you wouldn't want retweeted.)