I believe the original post stated budgetary constraints. So, taking the roll of the Devil's Advocate (somebody's gotta do it) here goes:
There's three main issues:
1. Intensity control. Unless you rig up a high-wattage dimmer circuit (which costs $$$) your only control over a work light is to adjust distance between it and the subject. That may be difficult/impossible unless one has a lot of space.
Peter: A 300W Home Depot worklight is adequately dimmed by a $6 Home Depot Dimmer. Actually, you could dim several of them from the same dimmer, should you want to.
2. Modifiers. Attaching gels, grids, softboxes, etc to work lights is difficult to do without overheating the fixture and risking a fire hazard, and you have to design all of your own attachment hardware, which takes time and $ to build.
Peter: Abslolutely true. However, with resourcefulness and patience, scrims and flags can be implemented at essentially zero cost. Bouncing, perhaps the simplest and easiest way of generating soft light is about as simple as it gets. Use a wall.
JW: Shooting with a bare bulb tends to result in harsh, unflattering light not well-suited for portraits.
Peter: Maybe. Depends on the lighting style you're after. Bare bulb shooting (point source) also leds itself to creative shadow generation, something that's much more difficult to make and is much more uncontrollable with soft light. Study the work of BW cinematographers from the 30's and 40's for examples of hard light (point source) creativity. It's not soft, but it looks great.
JW: 3. Heat. In a portrait lighting situation, your subject's going to be a lot closer to the business end of the lights than in a typical work situation, and your he/she will get hot, sweaty, and uncomfortable rather quickly.
Peter: Also true. Maybe. Depends on how big the room is, how many watts the lights are and how much they're dimmed.
The bottom line is that you can do whatever you want; this is a free country. But by the time you factor in all of the disadvantages and mounting hardware and extra labor involved in getting good portraits from work lights, you're not really saving much over strobes unless your time is worth zero.
* Not everyone can afford to spend hundreds on perfect tools.
* Time experimenting with unconventional solutions can result in huge leaps of learning, especially with regard to lighting.
* Safety is paramount, of course. Nothing you do should endanger anyone or anything. Common sense applies here.
I'm currently fooling around with lighting things with a single point source white LED that probably disappates about 1 microwatt. I'm learning lots and having fun, but I'm not trying to sell these images, nor am I keeping track of the time spent having fun.