PHILADELPHIA — Democrats marked a decisive turn in their campaign against Donald J. Trump this week, moving to recast the 2016 race not as a conventional battle between left and right but as a national emergency that requires voters of all stripes to band together against a singularly menacing candidate.

Abandoning their standard critique against conservative Republicans, allies of Hillary Clinton argued that Mr. Trump was not merely another champion of right-wing ideas, deserving of rejection for his views on the environment or health care.

Instead, in an onslaught of astonishing ferocity led by President Obama, they used their convention to portray Mr. Trump as a dangerously unstable figure and a friend of foreign despots like President Vladimir V. Putin of Russia. Some Democrats suggested Mr. Trump might have authoritarian impulses of his own: Prominent in Mrs. Clinton’s acceptance speech Thursday night was a pointed reminder that the American system was designed to prevent the rise of a dictator.

In effect, Mrs. Clinton and Democratic Party leaders signaled that they would seek to fight the general election, to some extent, in nonpartisan terms — as a clash between the broad mainstream of American voters and a candidate they argue would put the nation in jeopardy.