The Ukraine story has spurred Democrats to announce a formal impeachment inquiry of President Trump, and with those developments has come a noted rise in support for impeaching Trump.

But there remains considerable uncertainty among the American public about the Democrats’ underlying Ukraine accusations, according to a new poll. And importantly, a plurality seems to be internalizing Trump and his personal attorney Rudolph W. Giuliani’s dubious claims of potential wrongdoing by Joe Biden.

The Monmouth University poll shows people broadly disapprove of Trump’s phone call with Ukrainian President Volodymyr Zelensky, on which Trump asked Ukraine to pursue two investigations that carry potential political benefits for him. Americans say 63 percent to 21 percent that it is “not appropriate” for a president to make such requests of a foreign leader.

(Interestingly, though, Republicans say 43 percent to 31 percent that it is appropriate, despite the apparent invitation of foreign influence on a U.S. election, against which there are laws.)

But if you dig a little deeper, the Ukraine story doesn’t seem to have completely registered with people in the way Democrats would hope. The poll shows just 45 percent think Trump either “made any promises” to Zelensky or “put any pressure on” him to investigate Biden. Zelensky has said he didn’t feel pressured on the call. But shortly before asking for the investigations, Trump repeatedly noted how good the United States had been to Ukraine. There was no explicit quid pro quo, but Trump seemed to be linking U.S. assistance to his requests in a way that at least implied pressure.

Part of the reason for that low number is that many people simply haven’t consumed the news. About 1 in 5 Americans say they haven’t even heard about the Ukraine story. And in all, there are still more Americans saying Trump at least applied pressure on Zelensky (45 percent) than those who definitely say he didn’t (36 percent).

Plurality says Trump pressured Ukraine president to investigate ... -- "Do you think Trump made any promises or put any pressure on the Ukrainian president in return for investigating Biden, such as giving or withholding aid ... ?"

Here’s where the poll gets more depressing for Democrats.

That 45-36 split on whether Trump at least applied pressure on Zelensky is actually very similar to the split on whether Biden applied pressure on Ukraine to stop investigating his son — 42 percent to 37 percent. A plurality of Americans say it is “probably” true that Biden “put pressure on Ukrainian officials to get them not to investigate his son’s business dealings there.”

Except that that allegation is dubious at best. U.S. and Ukrainian officials have said the investigation of the company that employed Biden’s son Hunter Biden, Burisma Holdings, was dormant at the time that then-Vice President Biden was pressuring Ukraine to remove its prosecutor general. The prosecutor general himself wasn’t even investigating the Bidens, but rather the company. And even if the investigation had been ongoing, there was extensive pressure from the West to remove the prosecutor, who was accused of turning a blind eye to corruption. Biden’s effort was hardly extraordinary, relative to that of other powerful Ukraine allies.

One has an official rough transcript to support it; the other is a highly speculative claim. And yet, the American people appear to regard them approximately the same.

The 42 percent who believe the Biden claim may simply be Trump’s die-hard base, but it’s worth noting that it’s still more than those who disbelieve it (37 percent). Independents also say 43 percent to 31 percent that they believe it’s “probably” true. Even 1 in 5 Democrats (19 percent) believe it, suggesting it could factor into primary votes.

Giuliani has made clear since May that it was his intention to get people to focus on the Ukraine story, because it could help Trump in his reelection bid — apparently by neutralizing the Democrat who polls best against Trump, Biden.

The story isn’t reflecting well on Trump, certainly. But it does appear to be having some of the intended effect on Biden, despite the available evidence.