A broad swath of the nation’s leading chief executives dropped its opposition to tax increases on the wealthiest Americans on Tuesday, while the White House quietly pressed Wall Street titans for their support as well.

Before Tuesday’s about-face, the Business Roundtable had insisted that the White House extend Bush-era tax cuts to taxpayers of all income brackets, but the executives’ resistance crumbled as pressure builds to find a compromise for the fiscal impasse in Washington before the end of the year.

“We recognize that part of the solution has to be tax increases,” David M. Cote, chief executive of Honeywell, said on a conference call with reporters. “That’s the only thing that allows a reasonable compromise to be reached.”

Even as the Fortune 500 leaders announced their shift, the White House continued to work behind the scenes to woo some of Wall Street’s most powerful financiers — a group that had largely abandoned President Obama in his bid for a second term after supporting him in 2008.