shoot a line

old-fashioned To say something that is exaggeratedly boastful or untrue. Primarily heard in UK. Even then, the ageing poet was shooting a line about his supposedly "humble origins," when in fact he had grown up in a relatively prosperous home. The MP once again shot a line about the dangers of same-sex marriage, while offering nothing in the way of facts, statistics, or credible arguments.

If someone shoots a line, they say something that is exaggerated or untrue. He shot a line about needing new staff for his office.