Laser printers are particularly suited to solid-color jobs like charts and graphs, but not photos.
The most notable reason for this is that laser printers generate a lot of heat, and the heat changes what they can do. If you print 1000 (or even 100) copies of a photo and compare the first and last you'll see some stark differences, even with the best laser printer. In particular, the last print will show large patches of solid color, not smooth gradients of color. That is, the photo will appear blotchy. On a cheaper laser you'll also notice that many areas of the print have left the paper saturated and almost wet. The reason for this is that as the printer warms up the toner will also warm up, and the printer can't control the volume of toner being dumped onto the paper very well. So, you end up using way more toner than needed and getting poor results.
Another problem you'll notice is that the print looks different in different light: check it under fluorescent, incandescent, and daylight and you'll notice that some colors seem to look a little different. (A common one is that blues may look more/less purple.) It can be frustrating to be happy with the results when you first see them, and disappointed when viewed in a different environment! This change is known as metamerism and can be summarized as seeing a color shift in different light with a specific paper/medium combination. Changing paper may increase/decrease the amount of metamerism you see. This is something inkjets have pretty much solved with quality paper and effective inks, but toner in lasers is particularly subject to this problem.
The type of paper you print on is very important (and not just because of metamerism). Photo papers are designed to specifically absorb the medium without allowing it to spread. One of the reasons I bet you are seeing poor results is because the amount of toner being put out isn't just too much for the area, but it's spreading to make the surrounding areas feel muddy, too.
Working backwards, the next place to look at to controlling the print is the printer settings. Make sure that your printer is set to "photo mode" (which will try to better make subtle color changes to recreate the photo). Because you specifically see such a large yellow-to-orange color shift I wouldn't be surprised if the printer is set to "graphics mode" or "chart mode" (which purposefully tries to make the colors more bold and better suited to a handout at a meeting). Another place to be aware of in the printer settings is when selecting the "rendering intent." Use Relative Colorimetric or Perceptual (you might try both to see what you prefer); the others are not for photo use. Be sure to check other settings for reasonable values, too; most notably that the paper setting matches the type of paper you are using.
Are you sure the photo you see onscreen is a reasonable display of what the photo actually contains? You should really be working on a calibrated display to know for sure. When looking at the photo onscreen, move your head to the left and right, and up and down -- do you see any color shifts, most likely with colors becoming darker? If yes, your display simply isn't very good for color work because that little bit of change will make judging color very very hard. Most laptops have an unacceptable display, as will just about any cheap monitor. Visit dpreview.com and look at the bottom of one of their reviews and you'll find a black-to-white set of patches. Your monitor's brightness should be adjusted so that you can see every step of that gradient.
I assume you're using an LCD and not a CRT. CRTs are mostly gone, but there are a few holdouts, particularly at the office. IMO one of the best things about LCDs is how color-stable they are. CRTs will change color as they warm up at the start of the day, drift throughout the day, drift throughout the month, and continue to drift through their entire life. It's a constantly moving target to calibrate and work effectively on. LCDs on the other hand will take a little while to warm up, but are stable after that for most of their life. A quality LCD is going to do a better job of recreating color accurately out-of-the-box than a cheap LCD or CRT.
A worthy monitor should be calibrated for the best results. Using a hardware tool you can calibrate the screen to get the best possible results out of it and create a profile to help you see the best results it's capable of. Color management is another big topic unto itself, so I'll just say that if you're serious, hardware calibration for your monitor is an important step.
If you don't have a quality monitor (either an LCD that changes as you move your head, or a CRT), I would recommend getting one. If you can be confident that what you see on screen is an accurate representation of the photo and it's what you want to see in print, you've taken a big leap towards being able to get good results.
After you're confident you're seeing your photo accurately, get some good photo paper and the appropriate printer settings and arrive at the office early one morning before the laser has seen much/any use and print off your photo -- I bet you'll get acceptable results. (Not necessarily good, but acceptable.)