To sort of echo the issue of short-term need, figure that the difference in your income next season may more significant than the degree to which a needed is player is overpriced. If it was my team, I figure I have a swing that exceeds $1million if I were to relegate (I won't say exactly how much), so if I had to overpay less than $1 million if I thought that meant the difference between relegating and staying put, then of course I'd do it if I didn't have another option. A lot of the issue is risk assessment (how much does this player help, is he the missing piece, will you probably win without him anyway, etc.).
Otherwise, I don't overpay for players. There's a lot of fish out there to buy.
Don't ask what sort of Chunks they are, you probably don't want to know. Blowing Chunks since Season 4!