Following your Peers
Try to make your purchase price decision based upon as many concrete factors as you can gather.
Buyer in a Hurry
Any time a lengthy process is condensed into one or two weekends, the potential for mistakes is amplified. If not handled properly, a rushed purchase during a potentially stressful life change can often lead to buyer's remorse on multiple levels, including overpaying or choosing a home in the wrong area.
A buyer in a time crunch can mitigate the problem by working with an experienced agent who is active in the area.
Neighborhoods tend to have nuances and trends that are not necessarily obvious to most buyers. An experienced agent may have specific knowledge about a property that can be advantageous to the buyer, especially if they're on a tight timeline. It could be that they know of a house that's a better fit, or they might have a local's understanding of maintenance issues, for example.
Lowball Offer Backfires
Aside from the strong possibility of losing out to a higher bidder, the big risk is starting off on the wrong foot with the seller. If the seller gets insulted, or feels that yours is not a serious offer, they are less likely to respond with a reasonable counteroffer, and you've basically shot yourself in the foot.
While that doesn't mean the deal is dead, it can mean that the seller will be reluctant to negotiate when the buyer makes a serious offer. By starting off with a respectful offer, even if it's below the asking price, buyers create an opening to adjust the price downward as the deal moves toward closing.