I personally would be willing to pay $10 to someone who can offer to make microphone drivers work with one of my laptops under Ubuntu 10.10. I thought that other users could contribute to the same thing, and thus find a willing developer. Does there exist such a project(s)?
Such things have been tried, and generally were found wanting.
This sounds great in principle, but introducing bounties leads to conflict. For instance someone comes up with a really bad way to solve a problem, and the patch won't be considered by the maintainer. The maintainer's friend comes up with a better patch which gets accepted.
Who gets the bounty? If you say that the first person gets it, then the maintainer will get annoyed at pressure to accept bad solutions, and the second developer will get annoyed that someone was paid for bad work. If you say that the second person gets it the first person will cry "politics" and you've created bad blood. Either way you've created conflict.
Google Summer of Code appears to be doing a good job at it. Other attempts have not been very successful. Nothing comes off the top of the mind, but there were some attempts in that direction.
Foss Factory is another attempt but for GNU Hurd alone and not for open source projects in general. GNU Hurd will beg to identify itself as a Free Software rather than Open Source Software.
For your case, if you can bring other users to an agreement, and you end up hiring a developer, go ahead. Perhaps start off with the GNU Hurd style discussion and see where it takes to.
At present, it seems as though there are three (3) active sites that are worth considering:
- FOSS Factory
- PubSoft: Public Software Fund, Inc. (It could be defunct as there has been nothing new in the News section since 2007).
See alternativeTo for confirmation and further details. There have been several others, like BountySource, that are no longer in service. There is also some information in Wikipedia (but it really needs updating).