I believe the 'official' 37signals story is that when they were just a web design company they started building basecamp in their spare time, which wasn't very much and forced an efficient development process. However I believe they already had a popular blog which wouldn't hurt the process.
As a quick guess they may have done it with 20-40h of total development and design every week, and the marketing was likely done on less than that at first. Support would grow with the customer base.
This would of course work best if it's a second business line. If you have people who are dedicated to the startup full-time then you could work efficiently, but not if it's a challenging technical product (such as Facebook in recent years or MongoDB) or something very time-sensitive (the larger the perceived profit, the more competition you have).
The key is to leverage strengths - 37signals appears to have had good design and technical talent so they could pretty easily implement a simple product without struggling a lot, and they had a marketing channel ready to use. If you have a team with a similar ability to build and sell something that has value without putting in a lot of effort then you may be able to do the same.