(CNN) President Donald Trump has had no bigger international backer than Israeli Prime Minister Benjamin Netanyahu. Trump's policies, particularly where it comes to moving the US Embassy to Jerusalem and recognizing that city as Israel's capital -- and also where it comes to drawing a hard line on Iran's nuclear program -- are in alignment with Netanyahu's.

But there was a pall over their meeting Monday, since both men are beset by staffing issues, criminal issues, familial scandal and a skeptical press.

To help us break down the similarities -- and differences -- between Trump's problems and Netanyahu's problems, we have CNN's Jerusalem correspondent Oren Liebermann , who has written extensively about the Israeli Prime Minister.

Here's a transcript of our exchange, edited slightly for flow.

OL: The biggest difference is in the substance of the investigations. They are fundamentally different types of proceedings. Mueller's special investigation began with Russian election meddling and has proceeded along those lines; the police investigations against Netanyahu and his inner circle began as graft probes.

The end result may also be different, though that's unclear at this time. If convicted, Netanyahu will face a likely prison sentence, since these are criminal investigations. What happens if Mueller finds collusion between the Trump administration and Russia? What about obstruction of justice? Or perjury? We don't know the answer to those questions yet.

But from those initial differences, there are many similarities.

Both leaders' legal problems now involve members of their family and their inner circle. Netanyahu's wife, Sara, is now a possible suspect in one of the corruption investigations facing the Israeli leader, just as Jared Kushner has become involved in the Russia investigation. Members of each leader's inner circle have also become a part of the investigations -- Trump's confidants have been questioned by Mueller; Netanyahu's confidants have been named as suspects in the probes and have even turned state's witness.

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Both leaders have responded to the probes in much the same way -- blaming the opposition, blasting the media, slamming leaks and repeatedly proclaiming innocence. Even their language has matched up -- both have decried the investigations as media-fueled "witch hunts."

There is also one other difference worth pointing out. Trump is in office until after the 2020 election. The political reality for Netanyahu is quite different. If his coalition partners turn on him, he could be out very quickly.

ZW: A problem for Trump has been that his son-in-law apparently features in the Russia probe. And before the election, his son met with Russians promising dirt on Hillary Clinton. Netanyahu's family has also been drawn into scandal. Are the circumstances similar and are they involved in the Israeli government?

OL: Netanyahu's family isn't involved in politics the way Trump's family is involved. Though Netanyahu's wife is often by his side, she doesn't openly figure into the day-to-day operations of the Israeli government the way Trump's family does for the American government. Trump's daughter and his son-in-law have prominent, public roles in either the administration or the daily life of the President; Netanyahu's wife and children do not. Sure, Netanyahu's family makes headlines, but not nearly as often as Trump's family.

That being said, just as Trump's family has become a focus of the Mueller investigation, Netanyahu's family has become embroiled in the graft probes.

Sara Netanyahu is a possible suspect in one investigation, while her name features prominently in another.

ZW: Netanyahu has long weighed in on US politics, particularly where it comes to Iran. He was a supporter of Mitt Romney in 2012 and, perhaps even more so, of Trump's in 2016. How important is his relationship with Trump to Netanyahu in Israel?

OL: Incredibly important, and that's probably still an understatement.

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Trump gave Netanyahu a series of diplomatic and political victories, from recognizing Jerusalem as the capital of Israel to protecting Israel at the United Nations. Those were enormous scores for the Israeli leader, and he has tried to return the favor by repeatedly praising Trump and hailing the strongest ever ties between Israel and the US.

More importantly, Trump is popular with Netanyahu's voter base and vice versa. Even if Trump was considered wild and unpredictable at first, he is firmly in the pro-Israel camp now, so it's in Netanyahu's interest to play up the strong ties between the two leaders.

It's also worth remembering that this is the first time Netanyahu has had a Republican president. Up until now, it was either Bill Clinton or Barack Obama -- Netanyahu entirely missed George W. Bush's time in office.

ZW: How likely is it that Netanyahu survives this?

OL: In Israeli politics, it's never wise to bet against Netanyahu. He knows how to play the game of Israeli politics better than anyone ... and it is a brutal game. He's won four elections, and recent polling shows he would almost certainly win a fifth if elections were held today. He has the support of all of his coalition partners, which means he's in the driver's seat.

And yet each successive development in the corruption investigations of the Israeli leader is another blow to Netanyahu. Even if he has refused to back down, it becomes a little more difficult for his coalition partners to support him, and it becomes a political calculation of when to pull support. The closer the attorney general gets to possibly filing charges against Netanyahu, the harder it becomes to support him.

So why haven't they already pulled their support?

Because Israel's government is an entirely right-wing government, which means all the parties are pulling from generally the same voter base (with the exception of the ultra-Orthodox parties, who have their own voters). If one of Netanyahu's coalition partners pulls support for the Prime Minister, they may face a backlash from right-wing voters, upset that they toppled a right-wing government. That's why everyone is still supporting Netanyahu right now -- not because it's in Netanyahu's interest, but because it's in their own.

ZW: If, hypothetically, Netanyahu was forced out and his party lost power, what could it mean both for a Mideast peace process and also for the US and Iran?

OL: Every Israeli party -- left and right -- would continue lobbying against Iran. Maybe not as vocally, maybe not as openly, but they're all on the same page when it comes to viewing Iran as a threat, so that doesn't change.

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On the Mideast peace process, it depends on who would step in. Because of the way Israeli politics works, it's entirely possible that, even if Netanyahu was forced out, his own party would simply find a different leader. In this case, the peace process is probably dead on arrival, since many in Netanyahu's own party are far more critical of a two-state solution than he is.

If a centrist or left-wing party were able to win an election, then the peace process could still -- theoretically, at least -- proceed.

But the peace process doesn't only rely on the Israeli government. Washington would still have to find some way to coax the Palestinians back to the table, as there aren't many (if any) Israeli politicians they believe will readily make concessions in a peace process. And Mahmoud Abbas, the President of the Palestinian Authority, hasn't shown a willingness to make his own concessions for peace.