"Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid."
It's always important to read Scripture in context. The Senator seems to have skipped over some important verses which precede his citation:
"Jesus replied, 'If anyone loves me, he will obey my teaching. My Father will love him, and we will come to him and make our home with him. He who does not love me will not obey my teaching.'" -- John 14:23-24
John was pointing out the importance of obedience in truly following Christ and gaining "the peace which passes all understanding." This loving obedience seems a far cry from the Senator's approach to the teachings of his faith and his church.
Even Satan used scripture in trying to tempt Jesus in the desert.