Mr Osborne, the Chancellor, said that the project will be an "engine for growth” in the north of the country.
The route will pass though his constituency of Tatton and councillors today warned that while locals are in favour of any benefits to the local economy, there are concerns about the impact the project will have on the countryside.
The route of the planned HS2 high-speed link, including the northern sections announced today.
George Walton, the mayor of Cheshire East has warned that there will be "public outrage” over fears the train line will destroy countryside in the area.
However he told The Daily Telegraph that the "economic boost” to the area could make the project worthwhile.
"There will be a lot of public consultation,” he said. "It could be an economic boost to the north west. As with all these things unfortunately somebody is going to be affected, but that’s life.
"George Osborne will get a hard time from some people, but others like the business people could see it as a big boost.
"There is the danger it could affect the countryside, but high-speed trains are the future.”
Cheshire resident and Conservative councillor Rhoda Bailey said she was "totally against” the project.
"As a resident of Cheshire I’m totally against this. It is an enormous waste of money and I don’t think it should be despoiling the countryside,” Mrs Bailey said. "I don’t believe in the economic benefits and I don’t think it is financially viable.
"Some people are in favour but I think probably the majority will not say that there are going to be benefits. They think that we will get all of the pain but none of the gain.”
Andrew Kolker, Tory councillor for Dane Valley, said that although he has "doubts” about the project, he is "generally in favour”.
"I’m generally in favour if it brings economic prosperity to the north west,” Mr Kolker said. "Yes, I’m concerned about the environmental impact but you cannot make an omelette without breaking a few eggs.”
Mr Osborne said the case for HS2 is "compelling”.
"It is a controversial decision because building anything in this country, there are going to be people who object to it, and by the way, it goes through my constituency as well in Cheshire, not far from here,” Mr Osborne told BBC News. "I think the economic benefits to all the communities are pretty compelling.”