For better or worse, this is a Republican tax law. The vote totals speak for themselves. No Democrats or Independents voted for this measure.
The final vote totals were as follows: Source
The actual title of the law is “An Act to provide for reconciliation pursuant to titles II and V of the concurrent resolution on the budget for fiscal year 2018”. The original Short Title, “Tax Cuts and Jobs Act” was stripped by the Senate parliamentarian.