Investors typically hold diverse portfolios of assets, with the goal of reducing risk. While diversification is commonplace in investing, most of us have no diversification in our labor income streams: we work at one job at a time, for a single employer. However, the "returns" to a job vary like returns on investments, especially on non-financial dimensions (e.g., engagement, learning, co-workers, working conditions). As in investing, there is also a significant amount of direct financial risk in holding one job — the firm may impose layoffs or go out of business. Given the similarities between jobs and assets, why isn't there a similar impetus to diversify, i.e., why don't we all hold a portfolio of small jobs at the same time, with many different employers ?
Some workers — freelancers and independent consultants — do follow this diversified model, but it's hardly the norm of workers generally. Below, I lay out a laundry list of potential economic explanations for why the portfolio/freelancing approach is not more common. What's interesting to me both academically and as someone working at oDesk is that many of these points are not set-in-stone attributes of the productive process, but are instead things that smart features or policies might change.
Hiring a freelancer for a small project is like picking out a fancy restaurant; hiring a full-time employee is more like buying a house. The effort of searching and vetting (and thus the cost) is related to the stakes of the hire. However, there is no guarantee that those costs scale linearly with the stakes. Suppose it takes nearly as much effort to find a small job as it does to find a large job — then a portfolio approach will generate larger search costs per dollar earned in wages .
If you can make X widgets or Y schwidgets in 1 hour, it doesn't mean you can make X/2 widgets and Y/2 schwidgets in 1 hour. Every job has some fixed set-up costs — getting out the materials, remembering the key details, etc. The larger these costs, the less attractive the small job. On the other hand, productivity eventually wanes from boredom, physical fatigue, etc. ("I'm really getting bored with this TPS report — time for some Facebook"). The optimal job size (from a productivity standpoint) might be near or above the current 40 hours per week, 50 weeks per year paradigm, in which case going smaller means getting less efficient.
One of the advantages of team production is that workers can share knowledge with each other, motivate each other and generally create an environment where everyone is more productive than they would be working alone. There's no reason teams of freelancers working together cannot achieve the same complementarities with each other, but if these complementarities take time to develop, larger jobs become more attractive.
Once you get a sense of the character and reputation of some trading partner, you don't need to constantly monitor that person or firm; after some level of trust has been established, these costs would fall. This again pushes for larger jobs. This is probably clearer in terms of firms monitoring workers, since the big fear is shirking, but it does go both ways: workers need to make sure their checks don't bounce, that their employers aren't skimming from the 401K, that they're not using malk for the coffee service instead of milk, etc.
I do not think it is likely to find workers working simultaneously for direct competitors , as the interests of most firms are fairly orthogonal to each other.
At least in the U.S., at the present time, certain realities (health insurance, getting financial credit, etc.) are full-time employee-advantaged.
 Note that this isn't a theory of the firm argument or discussion. I'm assuming that one can be a full employee and reap all the benefits of firm organization/team production even with fractional employment.
 One of the reasons Mechanical Turk is semi-dysfunctional is that when problems arise (about the scope of work, payment terms, etc.), all the surplus generated by the relationship is quickly destroyed — one minute thinking, talking and haggling about a task that is paying pennies is likely to be economically wasteful. This was one motivation for hagglebot.