Trump partly won the White House by arguing deals such as the TPP hurt manufacturing workers in the Rust Belt, and many Democrats have opposed trade agreements on the same grounds. However, Democrats running this year in certain red states may have to tread carefully around the issue.

The president's decision to reconsider one of his first acts in office — withdrawing from the 12-nation Trans-Pacific Partnership — opens up another potential line of attack for some Democrats ahead of critical midterm elections in November.

Notable Democrats who found rare common ground with President Donald Trump on trade bashed his move Thursday to look at rejoining a massive Pacific trade deal .

In a tweeted statement Thursday, Sen. Elizabeth Warren, D-Mass., argued Trump's move to reconsider is a "ridiculous reversal" and a "slap in the face" to workers. The office of Sen. Bernie Sanders, a Vermont independent who caucuses with Democrats, tweeted that jumping back into the deal "would be a betrayal of American workers."

Both of those senators are running for re-election this year in solidly blue states. Sen. Jon Tester, a Democrat from Montana seeking another term in a state Trump won easily in 2016, had a more measured reaction but said the uncertainty could hurt farmers in his state. The agriculture industry largely benefits from lower trade barriers.

"Playing ping pong with TPP may be good for Twitter headlines, but it piles too much uncertainty on the backs of Montana farmers and ranchers," Tester said in a statement.

For his part, Trump tried to downplay the chances of the U.S. rejoining the TPP. In a tweet Thursday, he said he would only do so "if the deal were substantially better than the deal offered" to President Barack Obama.

Trump tweet

White House legislative affairs director Marc Short also stressed to reporters Friday that Trump only said he was willing to take another look at the deal. He did not say what specific action the White House could take related to the trade agreement.

It is unclear if the U.S. could even get back in on the agreement at this point. After Trump pulled the U.S. from the 12-nation deal last year, the remaining 11 countries agreed to a separate pact.

Trump's decision to reconsider the TPP came as his administration and China engaged in escalating tariff threats that many Republicans from agricultural states worried could hurt American farmers. Sen. Ben Sasse, R-Neb., contended Thursday that getting back into the TPP — a deal designed to counter China's rising influence — would be a better way to get back at Beijing for alleged intellectual property theft by Chinese companies.

Trump's comments about reconsidering the agreement came as he met with lawmakers from states with a farming presence. They expressed concerns about Trump's proposed tariffs leading to retaliatory measures from China that could hurt the agriculture industry.

Trade is one of several issues on which Trump has broken with the policies Republicans have traditionally backed. The president's opposition to the TPP distanced him from GOP congressional leaders and aligned him with numerous Democratic senators from states with significant manufacturing presences.

Sen. Sherrod Brown, D-Ohio, told CNBC: "Anything that looks, sounds or smells like TPP would be a disaster for Ohio jobs."

"The President must keep his promise to Ohio workers and stay away from this failed trade agreement," Brown said in the statement.

"If the President and Ambassador Lighthizer are serious about negotiating new, pro-worker trade agreements with our Asian partners, I am ready to work with them to secure the best possible deals for Ohio," Brown added.

In 2015, the GOP-controlled Senate passed legislation granting Obama the authority to expedite negotiations on TPP. Eight Democrats from states Trump would go on to win in 2016 voted against the measure: Tester, Brown, Bob Casey of Pennsylvania, Debbie Stabenow and Gary Peters of Michigan, Joe Donnelly of Indiana, Joe Manchin of West Virginia and Tammy Baldwin of Wisconsin.

All of those senators but Peters face re-election this year. Manchin's office declined to comment on Trump's move to reconsider TPP.

The offices of Donnelly, Stabenow, Casey and Baldwin did not immediately respond to requests to comment.

— CNBC's Eamon Javers contributed to this report.