I think Senate Democrats should at least try to counter the impression that they want the Patriot Act to expire, when in fact they want a three-month extension of the current law while discussions continue on changes to certain provisions.
Here's what I'd do: Summon the media, including local news organizations in Democratic senators' states. Then assemble as many filibustering Democrats as possible on the Capitol steps -- but at least forty-one (i.e., a number that exceeds the total needed for a filibuster). At this gathering, conduct a simulated roll-call vote on the three-month-extension bill, with the Democrats all voting "aye."
It's cornball, but it might be reasonably good TV, so it might get on the nightly news and have some effect on perceptions.
UPDATE: The Senate seems about to compromise on a six-month extension. Sanity prevails, apparently.