To approve, ratify, or allow something to pass or proceed through an official organized vote. Their party has been trying to vote through a number of tax reforms for the past 10 years. There's no way congress would vote such a contentious bill through at a time like this.
vote something through
to get something through a set of procedures by voting in favor of it. They were not able to vote the bill through. They voted through the bill.
To sanction, ratify, or approve something by voting: The Senate unanimously voted through the reforms. Legislators are voting through a bill banning smoking in most public spaces.