WI: The Lewinsky scandal went public during the 1996 election?

So let’s say during the 1996 election, Monica Lewinsky (or someone who knew of the scandal) came out with the scandal. How would this affect Clinton’s campaign for re-election? Does Bob Dole become the 43rd president of the US or does another democrat become president? What remains of Clinton’s legacy with only 1 term and a scandal?
 
I think in order to bring Clinton down, you not only need a scandal (and one that gets traction outside the far right) to break out, you need Gingrich and the GOP not to overplay their hand like they did OTL. Gingrich shot himself and the entire GOP in the foot by allowing the Government to shutdown, thus boosting Clinton's re election prospects. If this happens, and a Lewinsky scandal breaks no earlier than August or September and the GOP doesn't overreact to it, Dole can narrowly beat Clinton. As to how Clinton is remembered, I still think he's still regarded as one of the better Post War Presidents, so he'll at least be remembered better than Nixon, Carter, and even Ford, as he'll get some of the credit for the economic boom of the 1990s, an earlier Lewinsky scandal still not being seen as equivalent to Watergate in the eyes of the Public, and no huge foreign policy blunders (at least none that compare to the Iran Hostage Crisis or The Soviet Invasion of Afghanistan).
 
The website 538 posted an interesting article about the last government shutdown recounting their history, and stating that the whole government shutdown things were started by the executive branch (in 1980) to increase the leverage of the executive branch over Congress. This answers the political science mystery of why only the USA does this, because with separation of powers Congress and the Presidency are in continuous low level conflict over who runs the government, with the executive almost always prevailing in modern history, and the shutdowns are a tool of the executive branch. But what this implies is that the non-presidential party can never "win" a government shutdown, ever.

More strictly on topic, I lived through the 1990s and there were tons of accusations of sexual impropriety against Clinton. For whatever reason, they had no effect whatsoever and I suspect they increased his popularity, as did the Lewinsky scandal. What made Lewinsky different was the incontrovertible physical proof, along with the perjury, which meant that legally the House Judiciary Committee at least had to consider impeachment proceedings once the referral was made. Without either the physical proof or the legal referral this would have been buried like all the other scandals. Even with both elements the GOP would have found a way to keep it under wraps until after the election.
 
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