This explanation is oversimplified. Unionization had less to do with it than traditional DC power politics did.

There had been a small group of members of Congress who had been pushing for the merger of the various independent agencies into a single Cabinet-level department since the early 1990s. Partly this was due to a sincere concern over terrorist incidents like the first World Trade Center bombing in 1993 (http://en.wikipedia.org/wiki/1993_World_Trade_Center_bombing), and the belief that merging the agencies would result in greater efficiency and better performance in countering these threats. But it was also partly due to traditional DC power politics -- these congresspeople were on the hawkish, national-security-oriented end of the spectrum, and pulling together all the little agencies that tended to their pet issues into One Big Agency would give that agency more budgetary and bureaucratic clout, making their views more prominent. And making its leader a Cabinet-level officer would create a new seat at the cabinet table that they could all aspire to fill one day.

This faction was bipartisan. You can see this by looking at the makeup of one of its pre-9/11 projects, the Hart-Rudman Commission (see http://en.wikipedia.org/wiki/US_Commission_on_National_Secur...). You had Gary Hart and Lee Hamilton (Democrats) working together with Newt Gingrich and Jim Schlesinger (Republicans). But "bipartisan" doesn't mean that they represented the opinion of the majority of Congress or the country -- these were all people who had been working in and around national security issues since the 1960s and '70s, and they looked at issues with the perspective of people whose idee fixe is that America is not sufficiently organized like an armed camp.

They used the commission's final report, which it issued in February 2001 (http://govinfo.library.unt.edu/nssg/PhaseIIIFR.pdf -- warning, PDF) -- seven months before 9/11 -- to push explicitly for "an independent National Homeland Security
Agency (NHSA) with responsibility for planning, coordinating, and integrating various U.S. government activities involved in homeland security." But this proposal went nowhere, because nobody outside the national-security world thought the enormous costs and bureaucratic turmoil that unification would involve would be worth it. So this proposal looked like it was going to do what most blue-chip commission proposals do: collect dust on a bookshelf somewhere in Washington.

Then came 9/11, of course, and suddenly everybody in DC was running around shouting the same thing: Something Has To Be Done. The national-security faction, seeing this, was happy to dust off its report and say "We have Something That Can Be Done!" Which was a powerful thing to be able to say, at that moment -- while everyone else was running around trying to figure out how to respond, these guys had a plan all ready to go. When everyone else had nothing, they had Something.

And on top of that, suddenly the things that had looked so negative about their big idea -- the huge expense, the bureaucratic turmoil -- began to look positive; these things would mean everyone would see that not only was Something Being Done, but that this Something was Something Big. Which must mean it's also Something Important.

So Congress glommed onto the proposal, and the "National Homeland Security Agency," which had seemed like the ridiculous pipe dream of a bunch of defense obsessives, became the Department of Homeland Security that we all know and love today.