Members of Congress have begun a frenzy of lobbying to ensure that their pet projects and policy priorities are included in President Biden’s $2 trillion infrastructure and jobs plan, eager to shape what could be one of the most substantial public works investments in a generation.

Officials across the country are dusting off lists of construction projects and social programs, hoping to secure their piece of a plan aimed at addressing what the administration estimates is at least $1 trillion worth of backlogged infrastructure improvements, as well as longstanding economic and racial inequities.

Senior lawmakers have started collecting lists of requests from their colleagues for what should be included in the bill, while top White House officials are fielding a torrent of calls from rank-and-file lawmakers, all of whom have their own ideas.

“My phone is blowing up,” Pete Buttigieg, the transportation secretary, said in an interview. Nearly every lawmaker “can point to a road or a bridge or an airport” in his or her district that is in dire need of repair.

Representative Mikie Sherrill, Democrat of New Jersey, wants to tackle the Gateway rail tunnel under the Hudson River. Senator Mitch McConnell, Republican of Kentucky and the minority leader, has suggested that surely the “functionally obsolete” Brent Spence Bridge in his state should receive funding. And progressive lawmakers have a five-part wish list that includes lowering drug costs and providing a pathway to citizenship for undocumented workers.

Mr. Biden and Democrats have repeatedly challenged Republicans to engage in bipartisan negotiations. By incorporating Republicans’ proposals, including individual projects for their districts and states, Democrats hope to increase the political risks of voting against the bill. Some Republicans are already facing criticism for celebrating funding in the nearly $1.9 trillion pandemic relief package they unanimously opposed.