Do you get a good feeling when you find someone who goes above and beyond your expectations? I do! I recently dealt with a mid-size company (600+ employees) that consistently beat their delivery times. If they told me 3-4 days, it took two. If it was 2-3 days, I had the answer the next day. Having that kind of responsiveness to me gave me a great feeling about that company.
I used to wait tables in the last century (1990's). On occassion I would have to seve as the host. I was having trouble forecasting the wait time, and diners were getting disgruntled. A savvy manager pulled me aside and taught me a "trick of the trade". If the wait was about twenty minutes, he said tell the customer thirty. That way, he explained, if we called them in twenty minutes the customer felt like they got a table "early", and if we ran long and called them in thirty minutes, well, that is what the customer was expecting anyway.
It is a great idea to build expectations with your customers, as long as you can live up to them. It isn't cheating to build in a little flex time. If you think you can get back to them in a day, don't forget that Mr. Murphy and his infamous law is lurking to trip you up. Tell your client 1-2 days, or if there are other variables that could stretch your deadline, 2-3 days. I'm sure your customer would rather get something "early" the next day rather than "late" in two days.
I'm sure you don't need a reminder that this tool is only useful as long as it isn't abused. If you stretch your deadlines too far, your client will find someone else who can respond faster. This isn't a tool to allow you to take time off, but rather to cover the inevitable delays that creep into every part of the real estate business.
By building a reasonable timeframe with your client, and then consistently meeting or exceeding it, you will create a very rewarding relationship!