For either a VAT (value added tax) or a BAT (border adjustment tax), the only way politically to get from here to there is:
Let the tax plan be to begin in 2018 at only 2% (or 4%), and be raised by 2% increments each year, until reaching the 20% that is typical (such as by import duties) for other nations, our trade competitors.
This would allow even incorrect fears among importers that somehow they would bear costs to be dissipated, as they would see plenty of time for currency prices to adjust, and thus for price disadvantage to be avoided.
Is it a good idea?
Without getting technical, the answer is Yes.
Currency adjustment will happen, but also the fact the U.S. isn't 1/2 or more of the world economy will allow also real change in relative costs (other markets under generally free trade will blend the adjustment with other nations who are also customers).
Doing this gradually is the only smart way.
The BAT, like a VAT, and letting either of these replace much of domestic corporate taxes (such as for instance setting the BAT rate equal to the corporate rate), would help level the playing field, in that foreign production would be taxed at a rate much closer to domestic production.