Liz Iacobucci at The New Hampshire Labor News argues that it will:
Progress Massachusetts looked closely at Scott Brown’s voting record and came up with 40 bills that would have passed the Senate – if they hadn’t been killed by a Republican filibuster.  The list includes: 
  • Restoring American Financial Stability Act of 2010 (the original financial regulatory reform bill);
  • Creating American Jobs and Ending Offshoring Act;
  • Emergency Senior Citizens Relief Act of 2010;
  • American Jobs Act of 2011;
  • Rebuild America Jobs Act;
  • Middle Class Tax Cut Act of 2011; and
  • The Buffett Rule (a 30% effective tax rate on income exceeding $1 million).
All of those bills would have passed the Senate – if they had ever gotten to the floor for a vote.

If you've ever studied game theory, though, that conclusion seems a lot less persuasive. Republicans are almost certain to change their legislative strategy in response to the new rules. The outcome in this scenario is impossible to predict without more information.

Sarah Binder at The Monkey Cage puts it this way:
It’s tough to turn on a new rule and  calculate the effects that are likely to follow because it’s hard to know how senators will react.  A new rules regime—particularly one curtailing the right of extended debate under Rule 22—could encourage senators to aggressively avail themselves of every procedural avenue in the Senate rule book for obstructing the Senate.  For instance, the minority could become less likely to agree to invoke cloture on the motion to proceed, preventing the majority from calling up bills high on its agenda.  Or senators could become more aggressive in the demands they make on a leader as a condition for signing onto consent agreements.   Both scenarios suggest that filibuster reforms could bring  unintended consequences.

If labor sympathizers want to help working families, they'll have to do it the old-fashioned way – by swaying public opinion and helping to elect more liberal politicians.