WASHINGTON — When President Obama named Hillary Rodham Clinton secretary of state after the 2008 election, he turned a rival into a loyalist. But he also lost Mrs. Clinton as one of the most popular Democratic fund-raisers for his re-election effort, since the nation’s chief diplomat is not allowed to engage in campaigning.

The same restriction applies to the State Department’s ambassadors around the world, nearly two dozen of whom were fervent supporters of Mr. Obama in 2008, raising tens of millions of dollars for his first presidential campaign. He rewarded these backers with coveted diplomatic appointments to London, Paris, Tokyo and other capitals. Now, as federal employees, they are legally barred from reopening their gilt-edged contact lists.

It is one of the few handicaps of incumbency, and in a year when the Obama campaign says Mitt Romney and Republican-affiliated “super PACs” could raise more money than the president, it could be a significant disadvantage, if one difficult to quantify.