Reduce the colors with Image > Decrease Color Depth > X Colors (4/8 bit). - (shortcut Ctrl+Shift+6)  Choose a small number of colors - 16 or less is probably best. Choose the options shown to the left (Optimized Median Cut & Nearest color), then click OK.  Now increase the color depth again with Image > Increase Color Depth > RGB - 8 bits/channel. - (shortcut Ctrl+Shift+0)

The next step is to choose Effects > Image Effects > Offset.  Set Edge mode to Repeat, Horizontal to 0, and Vertical as far as it'll go (my image was 37 pixels high, the reason it shows 37 as the vertical offset).  This number will vary but slide it all the way over.

If you want horizontal stripes, set Vertical to 0 and Horizontal to as far as it'll go.

Then click OK. If you began with an image that was the size you want your background, you can save your stripes now. You could also add some texture or special effects.

I used my result for Flood Fill, selecting it under Materials as my current pattern, then setting the scale to 250 so my stripes would be larger.  Then I opened a new document the size I wanted my background to be and filled it with the striped pattern.

You can use your selection tool on just a portion of your stripes if you want to choose fewer stripes. Select the area you want to use before choosing the pattern in Material Properties.

Now, on to creating your plaid! Simply use the copy feature to copy your new striped background. Paste it as a new layer (Ctrl+L), then use the Image > Free Rotate (shortcut Ctrl+R) and rotate the top layer 90% left or right. Open your Layers Palette (F8) and reduce the opacity of your top layer until as much of the bottom stripe shows through as desired.  Merge your layers and save your plaid.

These graphics were done in PSP X; older versions show the opacity bar alongside each layer.