(CNN) This week, Democrats unveiled an agenda for the midterms that carefully avoided any mention of the issues that had led to accusations they'd been playing "identity politics" in recent elections. Their message, party leaders said, would be all economics, all the time.

But President Donald Trump is -- and has always been -- a culture warrior.

And he made an aggressive move to elevate those issues to the political forefront Wednesday by announcing via Twitter that he is banning transgender Americans from serving in the military.

It is reminiscent of George W. Bush political adviser Karl Rove's efforts to push a same-sex marriage ban in 2004 . Gregory T. Angelo, the president of the Log Cabin Republicans, said Trump's move "smacks of politics, pure and simple."

This time, though, top Democrats say they don't fear that a political debate over transgender rights will damage them in the Rust Belt. And some Democratic senators running for re-election in red states were sharply critical of Trump's move.

"Democrats need to show -- and can show -- that they can simultaneously fight for a society that is both more fair and more prosperous -- and drive home the fact that Trump is delivering neither," long-time Democratic strategist Ron Klain said in an email.

Democrats seen as prospects for the party's presidential nomination in 2020 immediately lambasted Trump's move. New York Sen. Kirsten Gillibrand vowed to introduce legislation to overturn it. California Sen. Kamala Harris called it "discriminatory, wrong, and un-American." Former Vice President Joe Biden tweeted that "patriotic American who is qualified to serve in our military should be able to serve."

The Democrats Trump is really seeking to put in an uncomfortable position, though, are the 10 senators up for re-election in states he won -- all of which have more white, Christian voters who polls show are more likely to oppose transgender rights.

Some of those senators also attacked Trump's decision.

"If a service member can do the job and is willing, they should be able to serve -- and they should be able to be open about who they are," said North Dakota Sen. Heidi Heitkamp, among the Democrats facing the toughest re-election battles in 2018.

"Decisions about military force posture and readiness are matters of life and death that should be among the most seriously considered by a president, and motivated by the best military judgment of the armed forces -- not by politics," Heitkamp said.

Indiana Sen. Joe Donnelly cited Alabama Republican Sen. Richard Shelby's criticism of Trump's transgender military service ban.

"When the stakes are as high as the safety and security of the United States, we should always have an open door for the best, most talented patriots," Donnelly said in a statement. "Military service should be about abilities, integrity, and performance, and I agree with my Republican colleague Sen. Shelby that everybody should be treated fairly and given a chance to serve."

"The decision announced by the administration today will prevent highly qualified, patriotic Americans from serving in our military," said Pennsylvania Sen. Bob Casey.

Ohio Sen. Sherrod Brown sounded a similar note, saying: "We should not turn away anyone who is willing and able to serve this country and help keep American safe."

Sen. Tammy Baldwin, D-Wisconsin, tweeted: "A ban against any patriotic American who wants to serve our country is wrong."

Democrats have at least two major recent data points that suggest the political tide has shifted on LGBT issues.

In Wisconsin -- one of the states Trump won that is holding a Senate contest in 2018 -- Baldwin, who became the first openly gay senator when she won the seat in 2012, is running for re-election.

And in North Carolina, the economic backlash against Republicans' transgender bathroom bill played a central role in GOP Gov. Pat McCrory's loss in his re-election bid in 2016.

Trump himself had campaigned on a promise to protect LGBT Americans -- although it was always through the lens of defending them from "radical Islam," rather than civil rights.

"This will become the latest example for voters that the GOP agenda is about keeping their most extreme base happy to protect Trump, not about delivering on the things people care about so we protect the middle class," said Democratic strategist Jesse Ferguson.

"If they think voters will reward them for an agenda that discriminates against people by firing thousands of them who want to protect our country instead of getting results on health care and the economy, they're tragically misreading America," he said.

In a sign that the politics of the issue might not be in Trump's favor, Republicans in purple states, including Arizona Sen. John McCain, criticized his broad tweets that left unanswered questions about whether thousands of transgender people currently serving in the military will be kicked out.

Missouri Democratic Sen. Claire McCaskill tweeted a link to McCain's statement and added, "What he said." West Virginia Sen. Joe Manchin also cited McCain. "I agree with Sen. McCain that 'any American who wants to serve our country and is able to meet the standards should have the opportunity to do so -- and should be treated as the patriots they are,'" he said in a statement.

What he said ⬇️➡️



STATEMENT BY SASC CHAIRMAN JOHN McCAIN ON TRANSGENDER AMERICANS IN THE MILITARY https://t.co/THzJblgnJ5 — Claire McCaskill (@clairecmc) July 26, 2017

Other Republicans in swing states who are on the ballot in 2020 also criticized Trump's decision. North Carolina Sen. Thom Tillis said he agrees with McCain. "Americans who are qualified and can meet the standards to serve in the military should be afforded that opportunity," said Iowa Republican Sen. Joni Ernst, a veteran. Sen. Cory Gardner, R-Colorado, told reporters, "I think anybody who wants to serve in the military should serve in the military."