draw a long bow
This is an expression that I thought was rather antiquated but which, to my surprise, is popping up with reasonable frequency, especially in political contexts. It means ‘to exaggerate or overstate’. And example might be I fear that the minister has drawn a long bow in claiming that the drought has been caused by the hot air of greenies.
You can draw or pull or shoot the long bow. A statement like the one above could be described as a good stretch of the long bow. I have commented before on the way in which we arrive at idioms based on the familiar practices of the day, but when times change we sometimes lose an understanding of how we originally fashioned these phrases. Now that horses are not the main form of transport we don’t understand phrases like give free rein. This expression goes back to medieval archery, although the phrase itself first appeared in the early 1700s. The image is of the bowstring being drawn back to give an exaggerated shape to the bow.