The “bromance” between Vladimir Putin and Donald Trump may be shocking, but it probably won’t change many votes. Photo: Natalia Kolesnikova/AFP/Getty Images; David Becker/Getty Images

In retrospect, the belief of so many political observers that Donald Trump’s outrageous comments about women, immigrants, Muslims, and other Republicans would “take him down” seems naive. Turns out an awful lot of Republican voters just don’t care for women, immigrants, Muslims, or other Republicans, either.

But one figure that Republicans presumably dislike more than all these objects of scorn is Russian strongman Vladimir Putin. So it was a bit surprising that Trump went on Morning Joe today and reciprocated Putin’s remarkable statements of appreciation and affection. Worse yet, he seemed to get into a bit of false-equivalency in suggesting that Putin’s alleged lethal violence against critical journalists was okay because, after all, America “does a lot of killing, too,” and at least Putin is a “leader,” which is more than he can say about “what we have in this country.”

Perhaps Trump cleverly insulated himself from intraparty blowback by couching his praise for Putin as a comparison to the hated Obama; after all, his audience is used to the 44th president being compared to Hitler and even the Antichrist. But Public Policy Polling thinks the Donald may have exposed himself to some damage:

The only poll I can find where we ever asked Putin's favorability it was 7/78 overall, 8/81 with GOP. Few people that hated in US — PublicPolicyPolling (@ppppolls) December 18, 2015

If his opponents play it right think Trump's Putin embrace has much much more potential to hurt him than support for Muslim ban — PublicPolicyPolling (@ppppolls) December 18, 2015

I dunno. If pressed on this issue, Trump would probably say only someone strong (i.e. himself) can stand up to America’s enemies, thus making Putin’s praise for his own self simply a token of the respect (and, implicitly, fear) he might inspire as president. Since it has become an article of faith among Republicans that Obama’s “weakness” is the single biggest challenge to U.S. national security these days, this essentially puerile argument might well set conservative heads nodding in approbation. After all, Putin envy has been a barely suppressed impulse on the American right for some time.

Beyond that, there is little precedent to show that voters care that much about an American politician’s overseas connections. Back in 1984, when North Carolina Governor Jim Hunt was challenging Senator Jesse Helms, he tried to take advantage of Helms’s obsession with subsidizing all sorts of nasty right-wing death-squad groups around the globe with an ad entitled “With Friends Like These.” It starred Roberto “Blowtorch Bobby” D’Aubuisson of El Salvador, and photos of his victims. It was a classic in negative advertising, and it didn’t move any votes at all. Neither, more than likely, would any effort to exploit the Trump-Putin “bromance.”