WASHINGTON — With the Republican-led filibuster of a Senate proposal to raise the federal minimum wage to $10.10 on Wednesday, Democrats moved swiftly to frame the vote as an example of the gulf that exists between the two parties on matters of economic fairness and upward mobility.

The question is not just one of money, they said, but of morality. And in doing so the Democrats returned to the themes that were successful for their party and President Obama in 2012 when they convinced swing voters that Democrats were mindful of the best interests of all Americans — not just those who are powerful and wealthy.

Speaking from the White House shortly after the measure was defeated 54 to 42, with 60 votes needed to advance, Mr. Obama admonished Republicans and called on voters to punish them at the polls in November. “If there’s any good news here, it’s that Republicans in Congress don’t get the last word on this issue, or any issue,” Mr. Obama said. “You do, the American people, the voters.”

“If your member of Congress doesn’t support raising the minimum wage,” he added, “you have to let them know they’re out of step, and that if they keep putting politics ahead of working Americans, you’ll put them out of office.”