Final push to install 8,500-tonne M27 underpass
Sam O'Neil owns a hair salon in Fareham and said the motorway closure would lose her about three days of business.
"The whole of December we are usually flat out," she said.
"This year we can't open it's just not worth it because people, clients and staff can't get here.
"It's going to have a massive impact and it's a real shame, the few days in between Christmas that we are open, financially really help to cover for the quiet January."
Andrew Jackson, National Highways programme manager, said: "Traffic levels are much lower over the festive period but there will be significant delays, and so our advice is to plan your journeys carefully.
"These works allow us to accelerate this important scheme and stimulate economic growth across the region by supporting the building of up to 6,000 new homes and the creation of thousands of new jobs."