Private organizations such as the SPLC and government agencies such as the FBI and the Department of Homeland Security already monitor the online activities of violent extremists. How hard would it be to collect that information in a database that could be used to check whether a would-be gun buyer harbors views that make him prone to murder?
Once the database is created, it can be regularly updated with the names of people who express views like Page's -- who talk about tyranny, hypocrisy, or a "sick society," for instance, or who quote inflammatory proclamations like this one, frequently seen on the T-shirts and signs of right-wing lunatics: "The tree of liberty must be refreshed from time to time with the blood of patriots & tyrants." I don't mean to imply that violent extremism is limited to the right; when you consider the ideas expressed by Ted Kaczynski, a.k.a. the Unabomber, it is clear that left-wing critiques of capitalism also lead to murderous violence.
I am not saying people do not have a right to express these alarming views -- just that if they do, they should not be surprised if they are turned away when they try to buy a gun. The Brady Campaign correctly says "it is time we acknowledged" that the Second Amendment "guarantees the right to keep and bear arms." But the Supreme Court has said that right is subject to reasonable regulations aimed at protecting public safety. What could be more reasonable than stopping dangerous people from buying dangerous weapons?