Many times I found myself wanting to go over budget in our search for a home. "It's only $30,000 over budget," I would think about a house, before my reasoning would kick in and remind me that we just couldn't afford it.
Try not to get into the habit of looking at houses beyond your budget. But if a home is on the market for long enough, and you love it, it may be worth making an offer.
The sellers could be motivated to close, and if you're a good buyer offering them terms they like, then you might just have an opportunity to get in there for a steal.
We would always patrol what was sitting for a few months and watch some favorites to see if there were price adjustments. This way, we were ready to pounce if a house came within our budget. When negotiating, always keep your number in mind and stay there.