New Skills for New Jobs Act This bill directs the Department of the Treasury to make quarterly matching payments to an eligible community college in an amount equal to the aggregate new job tax withholding matches received by the college for providing qualified training to job trainees under a state new jobs training tax credit program. Under a state new jobs training tax credit program, state income taxes that have been withheld by an employer on behalf of a trainee who has been employed are paid to the eligible community college, to the extent that the payment does not exceed the cost of qualified training specified in a contract between the college and the employer. The bill also provides funding for Treasury to carry out the program.