I don't think you are right. Where in the piece does he convey that impression?
The piece argues for the executive to be co-equal with the judiciary rather than subservient to it. The executive is, typically (depending on the state) elected by the people directly (but in some cases may not be). The executive of the nation is actually elected by the filtered votes of the people in the two-part process. None of this implies "democracy and not a representative republic". But, rather, both.
He is not arguing for all decisions to be made via popular referenda.
" ... an assault that continues, in this case, in contravention of the will of the people as expressed in Florida in the state legislature, by the governor, now by the Congress of the United States."
What has the Florida legislature expressed in this case?