In a series of phone calls, Democratic lawmakers and party officials have lobbied Mr. Biden and his top aides to seize what they believe could be a singular opportunity not only to defeat Mr. Trump but to rout him and discredit what they believe is his dangerous style of racial demagogy…

Mr. Biden’s campaign, though, is so far hewing to a more conservative path. It is focused mostly on a handful of traditional battlegrounds, where it is only now scaling up and naming top aides despite having claimed the nomination in April…

At the moment, Mr. Biden is airing TV ads in just six states, all of which Mr. Trump won four years ago: Michigan, Wisconsin, Pennsylvania, Arizona, North Carolina and Florida. The campaign included perennially close Florida only after some deliberations about whether it was worth the hefty price tag, and when Mr. Trump’s struggles with older populations made it clearly competitive, according to Democrats familiar with their discussions.

The campaign’s reluctance to pursue a more expansive strategy owes in part to the calendar: Mr. Biden’s aides want to see where the race stands closer to November before they broaden their focus and commit to multimillion-dollar investments, aware that no swing states, let alone Republican-leaning states, have actually been locked up.