Typically, we'd expect a Call of Duty campaign to last around 7 hours. They've never been lengthy titles. The longest according to players on HowLongToBeat is Black Ops 3, the campaign of which should take players around 9 hours to finish.
Modern Warfare 3's campaign should take you roughly 4-7 hours to complete. This is based on our run through the single-player component on Regular difficulty, as well as on community sentiment and reports.