The dollar tumbled against the yen and euro Friday morning after July’s U.S. job report brought more bad news. Private sector employers added just 71,000 jobs last month, and total nonfarm payrolls contracted more than expected.

“Overall, unquestionably a disappointing report,” economists at Capital Economics in Toronto wrote.

The latest sign that job growth isn’t keeping up sent the trade-weighted dollar index down to 80.3. That’s 9% below its peak just two months ago.

Stock market watchers call a 10% decline a bear market, and the term doesn’t seem too bold given the speed of the sentiment shift we have seen this summer.

In June, when the dollar topped out at $1.18 against the euro and 92 yen, the recovery in the United States looked more robust and Europe seemed on the verge of being sent to its death bed. Some euroskeptics were calling for the dollar to trade at parity with the euro.

But on Friday, the dollar approached $1.33 against the euro and 85 yen, which puts it near a 15-year low against the Japanese currency. Opponents of Fed chief Ben Bernanke’s expansive policies, rarely at a loss for words, were out in full throat.

“The smart money is quickly running away from the greenback,” said Peter Schiff, a longtime critic of U.S. fiscal profligacy who runs Euro Pacific Capital in Westport, Conn.

The unemployment rate hasn’t been below its current 9.5% in a year, and few forecasters expect to see it decline substantially in 2010. The failure of job growth to pick up has gotten officials talking about new ways to support the economic recovery.

Most notable was a paper issued last week by the president of the Federal Reserve Bank of St. Louis, James Bullard, in which he contended that the United States could face a Japan-style decade of economic stagnation. He said another round of Fed Treasury bond purchases offers “the best tool to avoid such an outcome.”

The markets don’t necessarily fancy the use of that tool, though, because it implies the government will print more money to provide short-term monetary stimulus – a tactic that skeptics see as having diminishing returns and, moreover, as debasing the value of the dollar.

“The printing of trillions of dollars to purchase of government debt will put serious pressure on the value of the dollar,” Schiff said.

Schiff and other dollar-debasement hawks note that the decline in the dollar recently has been accompanied by a rise in the oil price, to $82 a barrel. Another indicator dollar doubters watch, the price of an ounce of gold, has risen back above $1,200 for the first time since mid-July.

Of course, we have seen this movie before. The dollar’s decline will seem to be inexorable until suddenly conditions deteriorate somewhere overseas and the momentum suddenly shifts again. But for now the flight to safety seems to be running very much away from the dollar.