Depends on how high the resolution is on the original, and how you do the resizing. Also depends on the resolution of the printer. Resizing is a complicated function in terms of how you select the resolution. Maintain the total number of pixels the same. That means you must insure the pixels per inch is multiplied by the number you are reducing by. So if the original is 72 ppi and you reduce size by a factor of 10, the new ppi must be 720. But, some printers may not be able to reproduce 720 ppi.
Be sure, too, in your printer driver, to select top photo quality to get full resolution. Also, try printing on glossy photo paper, as regular paper limits resolution.
Now, as far as the original quality, if you are scanning a hard copy newspaper be sure you select a sufficient scanning resolution. If you are grabbing an image off internet, you must select a high res file to copy. If the original lacks resolution, reducing it will make it far worse.