The Chicago Bears are set to announce a $4.6 billion plan to build a new enclosed stadium and improved lakefront area with half of the money coming from taxpayers, sources said. But the team will have to overcome serious skepticism from several directions. The stadium itself would cost $3.2 billion to build, with another $1.4 billion in proposed infrastructure improvements, according to sources familiar with the plan who spoke to the Tribune on the condition of anonymity. The sources said the Bears plan to pledge $2.3 billion, which includes some financing through the NFL.