WASHINGTON — Each of the three previous presidents — two Republicans, one Democrat — signed an increase in the federal minimum wage.

Why not President Obama?

Given Mr. Obama’s emphasis on income inequality, and the popularity of an increase in opinion polls, you would think he would. But the story of recent increases underscores the indispensable ingredient he so far lacks: a Republican leader strongly motivated to make a deal over the party’s philosophical objections.

In 1989, it was a new Republican in the White House. President George Bush, while campaigning to succeed Ronald Reagan, had promised “a kinder, gentler America.” The Democrats then controlling both houses of Congress set out to take him up on it.

Mr. Bush drove a hard bargain on the minimum wage. He vetoed the first version Congress sent on grounds that it raised the wage by 30 cents an hour too much. But he eventually accepted a two-stage increase to $4.25 an hour on the condition that lawmakers include a lower “training wage” for teenagers.