What factors dovetailed around this time 1820-1832 to serve as an impetus to white males to push for thei right to vote?

There are a number of factors that are often credited with
causing a push for universal white male suffrage during this time.  Here are a few of
them:

• The Revolutionary War.  Obviously, this
  happened long before 1820, but the values expressed in things like the Declaration of
  Independence helped cause a desire for white male
  suffrage.


• Growth of the market economy.  As this
  happened, people began to understand that things that government did mattered to their
  everyday lives.  These included things like the creation of banks, the imposition of
  tariffs, and the building of internal improvements like
  canals.


• The rise of slavery as an issue.  This (which
  first showed up in the arguments that led to the Missouri Compromise) made many
  Americans, especially in the South, think that politics might be important to
  them.

Basically, then, the idea is that there
were more things going on that made politics seem important to the average white man. 
These things made him want to have the right to vote so he could have a say in the
government that ruled him.

If you have access to
The American Pageant by Bailey, et. al, read about this at the
start of Chapter 13, entitled "The Rise of Jacksonian
Democracy."