A senior Republican urged President Clinton on Sunday to reveal his relationship with Monica Lewinsky, saying he thought Congress would forgive the president if his story turns out to be a matter of sexual misconduct. Key Democrats agreed and said the sooner the better.

"If he comes forth and tells it and does it in the right way and there aren't a lot of other factors to cause the Congress to say this man is unfit for the presidency and should be impeached, then I think the president would have a reasonable chance of getting through this," said Sen. Orrin Hatch, R-Utah."I don't know anybody at the top of the system who really wants to see the president hurt in this matter," said Hatch, who is chairman of the Senate Judiciary Committee.

A similar message was coming from Clinton's Democratic allies in the wake of revelations last week that there may be physical evidence of a relationship between the president and Lewinsky, including a stained dress she has turned over to Independent Counsel Kenneth Starr.

As Clinton returned home from a weekend in New York, his senior advisers at the White House recognized that the growing sentiment for some sort of conciliatory statement, even among Starr supporters like Hatch, presented new opportunities.

"We're cognizant of a number of outside voices, both Republican and Democrat, urging some sort of public statement," said one senior adviser, speaking only on condition of anonymity. The adviser said it was too early to assess what Clinton's next move might be.

In Milwaukee at a meeting of the nation's governors, there was agreement that Americans, who have generally been critical of the uproar surrounding the Lewinsky affair, are starting to pay more attention.

"It's a sideshow, but a serious sideshow," said Colorado Gov. Roy Romer, co-chairman of the Democratic National Committee. "There's a higher level of interest than ever before."

Clinton has denied, both in public statements and in testimony in the Paula Jones sexual harassment case against him, having had a sexual relationship with Lewinsky. He will be asked again on Aug. 17, when he must testify for Starr.

Lewinsky, 25, also has denied having sex with the president, but last week received immunity from prosecution and reportedly will acknowledge a sexual relationship when she appears before Starr's grand jury.

Former White House senior adviser George Stephanopoulos said if Clinton had a sexual relationship with the former White House intern, it's time to come clean.

"Democrats believe the best thing for him to do right now is to go forward and tell the story," Stephanopoulos said.

"I would make peace with my wife and I'd stand up and say, `Here's the deal,' " Time magazine quoted Senate Judiciary Committee member Sen. Joseph Biden, D-Del., as saying. "Even though it might make Starr's case, no Congress would ever impeach him."

Hatch, speaking on NBC's "Meet the Press," said that if the president had a sexual affair with Lewinsky, did not commit more serious crimes such as obstruction of justice or suborning perjury and tells the truth about it, "it could certainly result in a non-impeachment."

Hatch said that if there aren't additional allegations of serious wrongdoing, "I'll certainly be there to try to help him if he will" tell the truth.

Starr eventually must present Congress with a report concerning the Lewinsky affair, the White-water land deal in Arkansas and other investigations concerning Clinton or the White House. The House then must decide whether to send articles of impeachment to the Senate, which could vote on removing him from office.

Stephanopoulos, appearing on ABC's "This Week With Sam Donaldson and Cokie Roberts," noted that "there's a lot of evidence out there" and it was "unlikely" that the president would continue to deny a sexual relationship.

If he does tell "the whole story," he said, "it will cut the legs out of Ken Starr's inquiry and there is no way that it will go forward in Congress." If he doesn't, "then the rest of his presidency will be crippled by impeachment proceedings."

Hatch said that with this session of Congress winding down and still no Starr report in sight, it was unlikely Congress would act this year.

But Rep. Bob Barr, R-Ga., a House Judiciary Committee member who has actively pushed for impeachment hearings, said those proceedings should take place regardless of whether the president changes his story and apologizes.

"Our job as members of the Congress is not to accept something on its face and say that's politically palatable," he told "Fox News Sunday."

Meanwhile, new information emerged about a conversation between Linda Tripp and White House presidential confidant Bruce Lindsey. It was Tripp's secretly taped conversations that spurred the Lewinsky investigation.

Her lawyer, Joseph Murtha, said that in 1994, when Tripp moved from the White House to a Pentagon job and was a potential witness in other controversies such as Clinton aide Vincent Foster's death, Lindsey advised her to keep quiet.

"In a non-menacing fashion, Mr. Lindsey told Linda that if she didn't keep quiet that she would be destroyed," Murtha said on CBS' "Face the Nation."

But Murtha added that Tripp did not take the statement as a threat.

William Murphy, a lawyer for Lindsey, said, "Any implication that Bruce Lindsey threatened to destroy anyone, including Mrs. Tripp, is false."

Murtha and another Tripp lawyer, Anthony Zaccagnini, also denied reports that Tripp once had considered stealing Lewinsky's dress. They said Lewinsky showed the dress, which she bought at The Gap, to Tripp on three occasions. Tripp "did see something that appeared to be a stain; what that stain is Linda doesn't know," Zaccagnini told ABC.