Obama has always been a fan of precedent; he thinks it armors him from criticism. For example the first time he made recess appointments -- absolutely required since his nominees have been filibustered at a rate far higher than prior presidents -- he appointed exactly the same number as Bush did in the same period of his presidency.
So I have a suggestion.
Obama is strongest when making direct appeals to citizens, something that the GOP has tried to minimize with comical effect. Here's my idea. I'm apparently bad at The Google because I can't figure out how many times G.W.Bush made prime time addresses and how many times the filibuster -- failing to reach cloture in the senate -- happened during his 8 years. But those two things are knowable numbers that could make a ratio. Suppose Bush did one TV address for every 20 filibusters. Obama could follow the precedent.
Not explicitly. That would be kind of like bullying or just being a jerk to make it an explicit rule. But he could do it implicitly. Drop enough hints through other people that maybe that's what he was doing. Every 20 filibusters (or whatever the real number is) he'd schedule a prime time TV address. He could talk about the important legislature that was being blocked by GOP obstruction. Talking heads on TV could speculate breathlessly about how this next vote would be the 20th filibuster and what would the president talk about this time. Democratic Senate leaders could tease Republicans about whether they want to trigger another prime time speech by the president.
At the very least it would make the unprecedented use of the filibuster less of business as usual and something to be discussed as actual news.
Assuming this makes sense. My crude research suggests that although cloture votes are succeeding less frequently for Obama, there may also be fewer of them overall. So perhaps senate Dems would have to bring to heat, about which they are very weak. In any case I offer this kind of thinking as a way to get outside the box of ordinary politics that's killing us one quiet cloture vote at a time.