White Hart Lane station will be redeveloped – with the creation of a newly-located station entrance, a new ticket hall and wider platform access. This redevelopment forms part of the regeneration plans for the west side of the High Road being led by Haringey Council. A planning application is expected later in 2015 with a target opening date of 2017.
The White Hart Lane station train service is coming under the control of London Overground in 2015 – with brand new and higher capacity trains, similar to the new Metropolitan Line trains, and station improvements planned. This important project is now being developed by TfL, Network Rail and Haringey Council.
http://www.tottenhamhotspur.com/new-scheme/well-connected/
According to the the microsite, the walk from the station to the stadium will be 2 minutes ... Not really sure it'll be that quick, more like 5 - but still, a quicker walk than Wembley.