I'm surprised more people haven't brought this up. All it will take to block any anti-gun bill in the Senate is for just one senator to step forward and use (or threaten to use) this tactic. They can't stop a filibuster without a 60% majority. People like Feinstein, Schumer and Boxer certainly don't have the numbers necessary to reach that. They would likely struggle to get a majority vote on any gun control legislation without a filibuster anyway. But they certainly don't possess the support needed to bring cloture and go ahead with a vote if just ONE senator steps forward to block it. And we have more than one who is willing to do that in order to protect gun rights. Tom Coburn (R) - Oklahoma and Rand Paul (R) - Kentucky are two that immediately come to mind who would do so in a heartbeat.
Just look at what a fuss Coburn made following the Virginia Tech shooting over a bill that was actually supported and endorsed by the NRA...
http://abcnews.go.com/Politics/OTUS/sen-tom-coburn-biggest-obstacle-gun-control/story?id=18040165#.UNxanWleF1O/
If he was willing to fight so hard against a bill that actually had the gun lobby's support, can you imagine how he is going to react to a proposal such as Feinstein's? Despite a slight democrat majority in the US Senate, the senate may prove a tougher nut to crack for the antis than the House when it comes to pushing gun bans...just because of the filibuster.
This is why I am not panicking over this situation and urging calm on the gun forums I frequent. Yes, be vigilant. Yes, contact your senators and representatives. Yes, join the NRA. But don't become so distraught over this issue that you make yourselves miserable or spend $100 on an aluminum USGI 30 round mag from CTD. As you can see, getting an anti-gun bill through Congress is going to be extremely difficult, even if it passes in the House and even if every democrat senator in the country is willing to vote yes on it (both of which is also highly unlikely).