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Despite a heavy push by President Barack Obama for a sweeping multinational trade deal, a majority of Americans echo the concerns of labor unions and a number of Democratic members of Congress that the trade accord will negatively impact U.S. workers and companies.

Two-thirds of Americans say protecting American industries and jobs by limiting imports is more important than allowing free trade so they can buy products at lower prices from any country, according to the most recent NBC News online survey conducted by SurveyMonkey from June 3-5.

And that sentiment is held across party lines, with majorities of Republicans, Democrats, and independents agreeing that limiting imported inexpensive goods from other countries to protect jobs from other countries is more important than being able to buy cheap goods.

Related: Nancy Pelosi in Balancing Act on 'Fast-Track' Powers for Trade Deal

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After a dramatic showdown in the Senate over giving the president "fast-track" aauthority to negotiate a sweeping multinational trade pact, the fight now moves to the House where the majority of Democrats oppose the legislation amid worries that the Trans-Pacific Partnership, a massive 12-nation trade accord, will cost American jobs and result in lowered middle class wages.

But that approval came only after the Senate initially blocked consideration of that legislation in a dramatic showdown that was seen as a stinging rebuke to the administration's efforts.

Meanwhile, Obama administration officials have been for weeks running a clear public relations strategy on trade, with the president talking the deal up in interviews last week with local news channels in states with large liberal populations and in previous interviews with David Letterman, MSNBC's Chris Matthews and recent interviews on NPR.

Related: Senate Blocks NSA Bill, Grants Obama Fast-Track Trade Power

Strongest support for allowing free trade comes among those with college degrees, with nearly 4 in 10 college graduates saying free trade is more important than limiting imports. Just 1 in 4 of those with some college and a third of those with high school degrees or less favor free trade over protecting American industries and jobs.

The NBC News Online Survey was conducted among a national sample of 2,153 adults aged 18 and over. Respondents for this non-probability survey were selected from among those who have volunteered to participate in the SurveyMonkey Audience panel.

Results have an error estimate of plus or minus 3.0 percentage points. A full description of our methodology can be found here.

The survey was produced by the Analytics Unit of NBC News in conjunction with Penn's Program on Opinion Research and Election Studies with data collection and tabulation conducted by SurveyMonkey. Analysis by the University of Pennsylvania's Program on Opinion Research and Election Studies.