Why didn't Republicans become the progressive/ liberal party?

[Battista Minola 1616]

How were the U. S. Whigs related to the British Whigs (the latter are the direct ancestor of today's Liberal Democrats)?

The US Whigs appear to have taken their name because of opposition to "King" Andrew Jackson, drawing a parallel to the patriots of the American Revolution who had revolted against King George III and were sometimes known as Whigs (because of course, Whigs on the British mainland were the faction opposed to absolute monarchy).