An attorney for President Trump once predicted that Robert S. Mueller III’s investigation would be done by Christmas — of 2017. When Rudolph W. Giuliani joined the president’s legal team in April, he predicted a resolution within “a week or two.” And on Wednesday, as news broke of Trump’s lawyers yet again rejecting Mueller’s offer of terms for an interview with Trump, Giuliani once again optimistically pegged an end date — Sept. 1.

Given all that, it’s difficult to believe that the end may be approaching. Alas, things may be coming to a head.

The most recent word from the Trump team is that it has issued what it considers something of a final offer to Mueller. In rejecting the special counsel’s latest proposed terms for an interview, The Washington Post’s Carol D. Leonnig reports, Trump’s attorneys maintain that questions related to obstruction of justice need to be off the table. “The multipage response represents what Trump’s lawyers expect to be their last word on Mueller’s request for a sit-down interview with the president in his Russia investigation,” Leonnig writes. Things can always change, of course, but continuing to negotiate now would risk looking like they had their bluff called.

Which means we could be at an impasse, with no peaceable resolution in sight. Each side seems to be waiting for the other to force a showdown over a potential subpoena of a sitting U.S. president — which would be just the second in history. And the prolonged nature of the whole thing is beginning to run into political realities, most notably the 2018 midterm elections, with the dynamics of the standoff shifting for both sides.

Let’s run through how.

The Trump side is broadcasting a desire to conclude this whole thing posthaste and well before the midterms. “This should be over with by Sept. 1,” Giuliani said Wednesday on fellow Trump attorney Jay Sekulow’s radio show. “We have now given [Mueller] an answer. Obviously, he should take a few days to consider it. But we should get this resolved.” Sekulow added in a lighthearted nod to Giuliani: “I think it will end soon. I never give dates; some of my colleagues give dates.”

All these efforts to set end dates have looked foolish in retrospect, so you have to think the fact that people like Giuliani keep predicting them is because their client demands it and they’re just trying to pacify him and his desire to be rid of the whole thing.

But if that’s really what’s happening, it would seem to strengthen Mueller’s negotiating hand. If he just waits Trump out — which, by outward appearances, could be part of what is happening here — perhaps Trump will eventually give in and just do the interview in the name of getting it all over with. The threat of a subpoena, after all, would potentially draw this out for weeks or even months more.

The New York Times, in its report on the Trump team’s latest counteroffer, suggested that Trump isn’t quite ready for that possible subpoena showdown and that he recently talked his attorneys out of just ending negotiations:

The negotiations have dragged on in part because the president’s lawyers are concerned that if he is interviewed, Mr. Trump could perjure himself. They had been prepared last week to tell Mr. Mueller that Mr. Trump would decline an interview, but the president, who believes he can convince Mr. Mueller that he is innocent, pushed his lawyers to continue negotiating.

The company line has long been that Trump actually wants to do the interview, but an equally — if not more — compelling explanation is that he wants to appear a willing participant. His insistence on more negotiation may be born more out of a desire to avoid a subpoena showdown that he could ultimately lose (after a long, drawn-out battle). Trump fashions himself a master negotiator, but he also has been known to drive a hard bargain and then declare victory without much of a shift in terms.

And under other circumstances, a subpoena fight would seem to be something Trump might actually want. It is maximum drama. It allows him to assert his presidential powers and beat the “witch hunt” in court. But, for some reason, we haven’t gone down that road yet. Regardless of Trump’s ego, it’s difficult to believe that’s only because he really wants to prove his innocence in a Mueller interview, but his attorneys have prevailed upon him to resist the urge.

But the prolonged nature of the whole thing also has some potential strategic value for the Trump team and negative consequences for Mueller. Polls suggest that Americans are gradually growing impatient with the investigation and, in some cases, are warming to Trump’s and his allies' arguments against its legitimacy. The longer this goes on, the more those feelings have a chance to fester, and the more people might begin to doubt that Mueller has the goods. Having the 2018 midterms overshadowed by the investigation may be something Trump wants to avoid, but it’s also a milestone for Mueller — two years and one full election cycle since Trump was voted into office. This actually isn’t that long relative to other similar investigations, but half the country seems to believe it has been plenty long.

“Team Trump’s hope presumably is they can string Mueller along until enough time has passed that the refrain of ‘Wrap it up’ will have more force and the public attributes to Mueller the blame for a delay from a subpoena battle,” said Harry Litman, a former Justice Department official. “But that battle, if it comes, means the probe hovers over the election. It’s a complicated series of calculations for both sides.”

Neither side has been willing to invoke the nuclear option — even as it may be inevitable (unless Mueller decides to give up). The decision here, as Giuliani and Sekulow emphasized Wednesday, lies with Trump and Trump alone. Perhaps Mueller thinks he can wait Trump out, and perhaps Trump is thinking the same thing.

It’s coming time for someone to blink.