For me this works only to stop future messages from that campaign. All the campaigns seem to buy and sell lists so I just get a different message from a different campaign at a different number. Here are the most recent offenders:

  Katrina Christiansen
  Harry Dunn
  Arizona for Abortion Access 
  Turnout PAC
  Yvette Clarke
  Josh Stein
  Ty Pinkins
  Democratic Majority
  Tammy Baldwin
  Democrats United