It seems unlikely. The Democrats proved over and over again that they'd roll over like dogs from 2001-2006 or so, and that's never appealing.
(Oh, and to be clear: we're only talking about the Senate here.)
Let's say the Democrats mount a principled opposition: civil liberties, "the war on terror" as an intelligence/police issue instead of a military one, etc…. It might help them somewhat, but I don't see them retaining their majority.
However, let's take up this POD: George Bush loses a speechwriter or two before 9/11 (Frum, or whoever) and his resulting speech is pretty bad. The country fails to rally around him.
Homeland Security fails in the Senate as the Democrats push an entirely different bill—a radical re-organization of the intelligence community. It creates an Intelligence Czar with budget power, breaks down the covert operations/analysis barrier in the CIA, shifts resources to create a CIA-DIA-State Department tripod (IOTL the DoD gets something like 80% of intelligence dollars IIRC), gives the NSA additional power while increasing oversight, and so on.
They present it as a defence against Republicans on civil liberties ("Big Brother") while also campaigning on it's new ability to handle terrorism with a much redone intelligence community. NSA absorbs minor agencies like the NRO, the CIA is given a way bigger budget for Humint and told to hand off technical information gathering to the NSA, the State Department gets beefed up, and specialist intelligence organizations (i.e the Energy Department) are given more weight…*this has a side effect of their opinion being listened to on Iraq (IOTL, again IIRC, they were the only to correctly state that the Iraq's did not have weapons of mass destruction). The CIA is pissed, somewhat, but also gets a bigger budget and the first Intelligence Czar is drawn from their ranks.
With Bush being less popular (worse reaction on his part to 9/11) and the Democrats pushing much harder on their bill Senate Republicans jump on their bill (which is the same, more or less) and the House passes the Republican version. Democrats, however, have won the media war on this and so even as they pass the similar Republican version they win control of it in the public's eyes.
With Bush having jumped on Homeland Security (IOTL he was hesitant, until it became a bandwagon—ITTL a similar situation happens except it blows up in his face) and historically unwilling to veto bills the new Intelligence Community for Defence of America (or some such stupid name) passes the Senate.
In 2002 the Democrats campaign on their having re-organized the intelligence community and preventing the rather stupid Homeland Security Bill. Republicans campaign much as they did IOTL, and the result is a draw…*almost. 51 Democratic seats in the Senate, within 10 seats of the House.