They spoke to shop keepers on Lower Northam Road and canvassed residents.
He said: "What's happening over all is that the number of private sector jobs is increasing, and that is true across most of the country.
"But we are not complacent about that.
"We now have a record number of new apprenticeships for young people and have a work programme to cut unemployment and get people back to work."
He also endorsed Mrs Hutchings because of her experience.
"She has been working hard in Eastleigh for a number of years, campaigning for local people.
"She has a record of campaigning for green fields, for disability rights, and with all her experience as a businesswoman, i think what more could you want."
Mr Hague is the latest political heavyweight to be deployed and follows Prime Minister David Cameron's meeting yesterday.
It comes after Deputy Prime Mininister Nick Clegg earlier this week launched the race for the seat, vacated by Chris Huhne last week.
The date for the election has been set for Feburary 28.
More news on the Eastleigh by-election
- Liberal Democrat Mike Thornton is new Eastleigh MP
- Clegg hails Lib Dem win in Eastleigh
- New Eastleigh MP's pledge to voters
- I'm overwhelmed by victory, says MPs wife
- Full list of Eastleigh by-election results
- Defeated Tory candidate made a swift exit
- Mike's night but UKIP almost took centre stage
- Lib Dem Mike Thornton is Eastleigh's new MP