WASHINGTON — On the surface, President Donald Trump's latest defense appears half-defiant, half-wild.

On Thursday, he undertook the very action that House Democrats have said was an impeachable offense when he did it privately on a phone call with Ukrainian President Volodymyr Zelenskiy in July — only this time, he did it publicly.

As he departed the White House for Florida, he called for two countries — including one of America's top adversaries — to probe the family of one of his potential 2020 rivals, former Vice President Joe Biden.

He said Ukraine should investigate the Bidens, then added, "And, by the way ... China should start an investigation into the Bidens, because what happened in China is just about as bad as what happened with Ukraine."

If Trump were subject to traditional legal jeopardy, it would be highly unusual — not to mention, counterproductive — to brazenly and publicly recommit the possible crime for which he was under investigation. But the Justice Department has opined that the president cannot be indicted for any reason, and Trump has no concern that he will be held accountable in a courtroom anytime soon.

So what he is facing is an inherently political impeachment process informed by public opinion. He needs to keep Republican voters in his corner. If he can do that, their elected representatives in the House — and, more important, in the Senate — will have a harder time abandoning him.

He's deploying a two-pronged strategy, said Republican strategist Ron Bonjean, who helped shepherd Supreme Court Justice Neil Gorsuch's nomination through the Senate and has worked as a leadership aide in both chambers of Congress.

"With these type of stakes, you're either hitting the other side or you're getting hit, and he's trying to turn the coverage toward him hitting, and it's working," Bonjean said of one prong. "The other is for him to normalize" his efforts to push other countries to investigate the Bidens.

Full coverage: Trump impeachment inquiry

Trump didn't even do much to distance himself from the politics of the investigations he is seeking.

"I think Biden is going down," he said when asked about the former vice president's remark that his family wouldn't be taken down by the president. "And I think his whole situation — because now you may very well find that there are many other countries that they scammed, just like they scammed China and Ukraine. And basically, who are they really scamming? The U.S.A. And it's not good."

The obvious gamble is that voters will see his public pleas as evidence that he has nothing to hide, rather than legitimizing the allegation that he is abusing his office to pursue a personal political vendetta.

"What he’s basically saying to the public is, 'If this was so bad, I wouldn’t be talking about it,'" said Michael Steele, a former Republican National Committee chairman and vocal critic of the president. Yet, "in effect, all he’s doing is confirming and affirming what people are alleging he’s done that is problematic."

What Trump has to worry about is that a much greater share of the public will decide that he has violated his oath of office, abused his power as president and should be removed from office. If that happens, both his re-election and his ability to keep Republican lawmakers in his corner are at risk.

There are signs his remarks may well add to his troubles in the House.

"Someone should inform the president that impeachable offenses committed on national television still count," Hillary Clinton, who watched Trump publicly ask Russia to find and release her emails during their 2016 campaign fight, wrote on Twitter.

But for now, the president clearly is focused on the public-relations war, which first means making sure GOP voters don't let Republican senators walk away from him and ends with trying to survive impeachment with enough strength to carry the electoral college in 2020.

His take is that he did nothing wrong, not that he didn't do it.

If it works, Republican voters will stand by him, and that will force his party's lawmakers to do the same. Technically, the initial test is in the House, where Democrats have enough votes to impeach him without Republicans, but the count of GOP defectors will be closely watched. To avoid removal from office, Trump has to make sure he doesn't lose 20 senators — a number that would be easy for him to hit if there isn't a major shift in public opinion.

But his tack is fraught with peril: It may not take many Republicans in Congress turning on him to convince more voters — and other GOP lawmakers — that what he's done is, in fact, an abuse of power that threatens the sanctity of national elections, underscores why the founding fathers warned against foreign entanglements, and jeopardizes Americans' faith in their republic.

The jury of Republican senators, and some GOP voters, may not take kindly to him bragging about his actions.

With House Democrats bearing down on impeachment, and knowledgeable State Department officials lining up to testify on Capitol Hill, Trump may have little choice but to follow this path. His White House released evidence, in the form of a summary of his comments on the summer call with Zelenskiy, that he had sought a probe into the Bidens as one of two favors discussed in conjunction with the release of $391 million in U.S. aid to Ukraine that he had stalled.

It's worth noting that, in addition to the money for Ukraine, Trump currently has the leverage of hundreds of billions of dollars on tariffs on China as a bargaining chip as he seeks a Biden investigation in that country. While extortion or bribery could be part of a charge, it's not necessary for an article of impeachment. One could be drafted and voted on simply on the use of his office to pursue personal political gain.

Steele said Trump's approach is a bad bet — it's a defense that relies, he said, on voters being "wholly ignorant of the facts."