It also offers the first sign that Democrats see another chance to try to turn the president’s vaunted political apparatus into a more permanent grass-roots movement. A similar attempt after Obama’s 2008 victory produced mixed results.

The plan calls for the former campaign organizers to orchestrate protests in front of lawmakers’ offices and set up phone banks to call constituents, among other things, according to people familiar with the evolving strategy.

The effort will focus on GOP lawmakers from multiple states — including Kentucky, Maine, North Carolina, Ohio, Pennsylvania, Tennessee and Virginia — that are home to Republican leaders or members who are considered moveable on taxes. It also involves a new Web site, theaction.org, which will serve as a hub for the tax fight and future campaigns.

The plan reflects the post-election confidence that Obama has displayed in recent days — a sense of strength that was nonexistent the last time he tried to strike a deal with GOP leaders in the ill-fated summer of 2011.