A Senate committee is set to vote on the issue Wednesday.

The survey of 800 registered voters -- done by Public Opinion Strategies and the Mellman Group -- found that 70 percent of voters support Congress passing the legislation and 72 percent view the bill's passage as an "important accomplishment."

In fact even a "majority of smokers" support the bill, said advocacy group Campaign for Tobacco-Free Kids, and support for the measure seems to cut across ideological lines, with 72 percent of Republicans, 71 percent of Democrats and 68 percent of Independents favoring FDA regulation of tobacco.

"There are few issues before Congress on which you'd find such strong consensus across regions and across party lines," said Matthew Myers, president of the Campaign for Tobacco-Free Kids. "Americans agree that it's time for Congress to address the nation's number one preventable cause of death and end the deadly status quo that allows tobacco companies to target our children and mislead the public."

However, policy experts have warned that, if the FDA were given authority over tobacco products, including cigarettes, it would have to ban them outright as harmful drugs and/or devices, as the agency is bound by law to approve only those products under its purview that it finds to be "safe and effective."

Specific findings from the survey include:

-- 80 percent support restricting tobacco sales to children by requiring ID checks for younger buyers and fining retailers who sell tobacco to minors.

-- 76 percent support restricting tobacco marketing aimed at children such as limiting advertising in magazines with a large percentage of readers under age 18.

-- 68 percent support preventing tobacco companies from making claims that some products are less harmful than others unless the FDA determines those claims are true.