Former Vice President Joseph R. Biden and his son Hunter could be forced to testify if the Senate ends up holding an impeachment trial of President Trump, say congressional aides who questioned whether Democrats have thought through the full implications of their impeachment drive.

Not only could Mr. Biden be forced to be in D.C. at a critical moment in the presidential campaign, but so could many of his chief rivals — the half-dozen senators also vying for Democrats’ presidential nomination, impeachment experts said.

For that matter, if the House chooses to impeach Mr. Trump on charges stemming from the special counsel’s Russia investigation, aides said it could open the door to witnesses such as fired FBI Agent Peter Strzok or even major figures from the Obama administration.

Mr. Trump could even be present for the entire spectacle. Experts said the Senate would have a hard time refusing him if he demanded to confront the witnesses against him.

“I don’t think the Dems have thought this through at all,” one staffer told The Washington Times.

Democrats have control of impeachment in the House, where it takes only a majority vote to pass articles of impeachment, which are effectively a political indictment.

Should the House take that step — Speaker Nancy Pelosi insists she’s not made up her mind, but she and her troops appear to be rushing that way — the matter would then go to the Senate, where a trial is held, the senators sit as a jury, and it takes a two-thirds vote to convict and oust the president.

Republicans have a majority in the upper chamber, giving them full control over what an impeachment trial would look like.

Over the course of nine pages the Senate Manual lays out some guidelines: All senators take a special oath of duty for the trial. The Supreme Court chief justice presides. And witnesses can be compelled to testify.

Sen. Lindsey Graham, South Carolina Republican and chairman of the Senate Judiciary Committee, said this weekend that the GOP would certainly force the whistleblowers who have accused Mr. Trump of improper behavior in his phone call with the Ukrainian president to testify publicly.

He also suggested Rep. Adam B. Schiff, the California Democrat who Mrs. Pelosi has spearheading the impeachment push right now, could become a witness in any impeachment trial given revelations he hid interactions with one of the whistleblowers.

Jonathan Turley, a law professor at George Washington University who was part of the defense team for a 2010 impeachment of a federal judge, said much of what an eventual trial looks like would depend on the articles the House passes.

If the focus is on Mr. Trump’s attempt to have Ukraine investigate the Bidens, for the vice president’s role in getting a prosecutor fired and possibly protecting his son’s business dealings there, then the two men might expect to have to testify.

“If Trump is impeached on the Ukrainian call, the Bidens would be fair game, particularly Hunter,” Mr. Turley said. “While I do not agree that the evidence supports the allegation against Biden in pushing the termination of the prosecution, there is little question that the Hunter Biden deal smacks of profiteering on his father’s position.”

Things could get even crazier if articles of impeachment include the special counsel’s investigation into Trump’s behavior concerning Russia.

Mr. Turley said that could give Mr. Trump a chance to raise all the lingering questions about decisions made by President Barack Obama’s Justice Department and the FBI. Several ongoing investigations are expected to find major fault with how investigators pursued Mr. Trump, beyond the already embarrassing text exchanges between Mr. Strzok and his paramour, former FBI lawyer Lisa Page.

He said that might explain Mrs. Pelosi’s reluctance to pull the impeachment trigger over the Russia accusations, and her insistence on trying to keep things focused on Ukraine.

“The optics of this Senate trial could be quite grotesque. You could have the Democrats beating Trump with the Ukraine call, you could have Trump beating the Democrats up over Biden,” he said.

The Senate faced a similar possibility in 1999 — the last presidential impeachment trial, involving President Clinton, who belatedly admitted to having had sexual encounters with intern Monica Lewinsky in the Oval Office.

The House passed two articles of impeachment: lying to a grand jury and obstructing an investigation.

When the articles reached the Senate, then-Sen. Trent Lott of Mississippi, the GOP majority leader, struck a deal with the top Democrat at the time, Sen. Tom Daschle of South Dakota, to prevent things from spiraling out of hand.

One major decision was to rule out having witnesses testify to the chamber.

“I just said ‘No, I’m absolutely opposed to that,’” Mr. Lott told The Times last week as he recalled the discussions. “To demean the institution by such a spectacle was totally inappropriate.”

He took serious heat, particularly from House Republicans who’d pushed the impeachment and who felt Mr. Lott was hamstringing their case.

But the former senator says there were never going to be 67 votes to convict Mr. Clinton — “the utmost I thought we might could have gotten were 61 or 62,” he says — no matter what he did, so there was no point to a divisive floor battle.

That’s not to say there weren’t flare-ups.

Senators did debate whether to have Ms. Lewinsky publicly testify about her encounters with Mr. Clinton. That motion was defeated, 70-30.

One of those who did vote in favor of the motion was Sen. Mitch McConnell, the Kentucky Republican who is now the majority leader, and who will have the most say in what happens.

“The majority leader has a lot of leeway, and Mitch McConnell knows the rules of the Senate as well or better than anybody I know,” Mr. Lott said. “They could have a vote to just dismiss [the articles], they could have a truncated process that would take a quick look at it and go through votes, or they could go through the process we went through that lasted almost a month.”

Mr. McConnell has said if the House does impeach Mr. Trump the Senate has to take the matter up, though he hasn’t said what a trial would look like. However, a new campaign has made clear what will be the outcome.

“The way that impeachment stops is a Senate majority with me as majority leader,” the Kentucky Republican vows in the ad.

Jim Manley, a longtime Democratic staffer who was working for Sen. Edward M. Kennedy at the time of the Senate’s Clinton trial, said bipartisanship defined the process in 1999.

A key moment came early on, when Mr. Kennedy, a liberal icon, and Sen. Phil Gramm, a conservative champion, both voiced support for keeping a lid on things and ensuring the Senate wasn’t wounded by the spectacle. Mr. Lott and Mr. Daschle struck an agreement to make good on that sentiment.

Mr. Manley said he hopes Mr. McConnell follows Mr. Lott’s lead — but he’s not confident.

“Hope springs eternal, but the fact of the matter is, for better or worse, Mitch McConnell is no Trent Lott,” Mr. Manley said. “If Sen. McConnell wants to have that stain on his record he’s able to do so.”

One key difference between this time and last time is the political breakdown. Then, it was a GOP Senate trying a Democratic president, with no chance of winning the two-thirds vote needed to oust Mr. Clinton.

Now it’s a GOP Senate that would be trying a Republican president impeached by a Democratic House that most of the Republican senators think has gone off the rails. The incentives to allow a spectacle to embarrass Democrats might be too much to resist.

Michael Gerhardt, a constitutional law professor at the University of North Carolina and author of “Impeachment: What Everyone Needs to Know,” said the GOP will have a lot of leeway to structure things how it wants, including rules for witnesses and evidence.

“Democrats could object, but they’re in the minority and there’s not a lot they can do about that,” he said.

That also likely means the White House will play an outsized role in calling the shots. If the president wants to personally confront the witnesses, for example, the Senate would be hard-pressed to stop him.

“I expect it’ll be Sen. McConnell’s show. But the president might well say ‘I want to be there, I want to ask questions,’” Mr. Gerhardt said.

Otherwise, Mr. Trump would be ceding the spotlight to his potential Democratic presidential opponents.

“It will be televised,” Mr. Gerhardt said.

Mr. Lott said the conversation in Washington appeared to take it as a given House Democrats will pursue impeachment. He said as someone who’s been through the process, he would urge them not to do it.

“My advice would be calm down, shut up and start passing some legislation that’s in the best interests of the country,” he said.

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