Americans are concerned over China's growing economic strength, and most want U.S. leaders to be tough with China on trade and economic issues, according to a new survey.

A full 78% of Americans say the large amount of U.S. debt held by China represents a serious problem, while solid majorities cite the outsourcing of jobs and the trade deficit as worrisome issues.

The survey, conducted by the Pew Research Center, also indicates that Americans are much more likely to be concerned by China's growing economic might than even its military prowess.

The U.S. economy dwarfs that of China, which surpassed Japan in recent years to become the second largest in the world. But China is growing much more quickly than the United States. Even in a slowdown, China's economy still registers more than 7% annual growth, compared to 2% or 3% for the U.S.

At the same time, the U.S. trade gap with China widened to a record $280 billion last year, and is on pace to get even bigger this year.

Even though they regard China's economic rise as a threat, Americans ascribe some positive attributes to China's population. A majority of Americans describe the Chinese people as hardworking, competitive and inventive. Most Americans also believe economic growth will result in a more democratic China.

Still, only 26% of Americans say that China can be trusted a great deal or a fair amount.

Related: Meet China's middle class

Relations between the two countries, especially on issues of trade, have been in focus in recent days.

The Obama administration filed a complaint Monday with the World Trade Organization alleging that China has illegally subsidized automotive exports and undercut American suppliers.

Some observers characterized the complaint's timing as politically motivated. But Election Day could bring real changes to the U.S. relationship with China.

Mitt Romney, the Republican nominee, has taken a combative stance toward China. The former Massachusetts governor has pledged to label China as a "currency manipulator" and hit the country's exports to the United States with tariffs.

Some observers worry that if Romney follows through with his plans, a trade war could erupt between the two economic mega-powers.