"Pushful" is a word I have never seen before, and seems
a clumsy, poor choice, particularly from Mencken.
I think "aggressive" would be my choice.

" It was reserved for Andrew Jackson, a man genuinely of the people, to lead and visualize the rise of the lower orders. Jackson, in his way, was the archetype of the new American—ignorant, pushful, impatient of restraint and precedent, an iconoclast, a Philistine, an Anglophobe in every fibre. "

AHD4 lists it as an adjective and defines it as 'pushing.'

I have a little trouble with 'pushing' as an adjective given Mencken's usage. I find 'pushful' to be somewhat different in connotation from 'aggressive,' but.

http://www.bartleby.com/61/50/P0675000.html

In the above quotation, I think Mencken was not justified in calling Andrew Jackson "ignorant". Undoubtedly he had little formal education, but he had to have intelligence and ability to become President of the United States.(Not like some of his successors who were stuffed shirts picked
to front for political groups.)