Updated: 4:30 p.m. | Newark Mayor Cory Booker has filed papers to run for Senate. The Huffington Post first reported the news.

It is another instance of incremental pressure Booker has applied over the last month on Sen. Frank R. Lautenberg, a fellow Democrat. A big question among New Jersey Democrats is: Are these moves encouraging Lautenberg to step aside, or is Booker alienating the incumbent to the point that Lautenberg will double-down and run for re-election?

Earlier this week, Fairleigh Dickinson University released a poll that showed Booker leading Lautenberg in a head-to-head matchup. Also, Sen. Jay Rockefeller’s, D-W.Va., retirement announcement Friday morning sparked chatter on Capitol Hill that Lautenberg is most likely the next senator to announce his retirement.

A “senior adviser” to Lautenberg lashed into Booker in comments to Politico, calling him “self-absorbed and disrespectful.”