They will reflect on the peace plan that will probably have been made public by the Trump administration a day or two earlier.
No doubt there will be lots of eulogising and talk of "historic" opportunities.
For both leaders the hullabaloo will be a welcome distraction.
The Senate will continue to consider Mr Trump’s impeachment.
The Knesset will continue to consider the implications of charges of bribery faced by Mr Netanyahu.
What the peace plan is unlikely to do, however, is advance the cause of peace.
No Palestinian leaders will be at the White House. Were any to be invited, none would attend anyway.
They regard Mr Trump’s attitude to the conflict as wholly one-sided, impossibly biased in Israel's favour.
If the leaks in Israel are true the peace plan will allow the Israelis to annex most of their West Bank settlements.
In return there will be the promise down the line of some kind of Palestinian state based on roughly 70% of the West Bank.
The Palestinian leader Mahmoud Abbas has warned if the rumours are true he may collapse his Palestinian Authority administration and force the Israelis to take over all the responsibilities of an occupying power.
King Abdullah of Jordan has warned that the proposals may put his country’s peace agreement with Israel in jeopardy.
Given the risks, one could be forgiven for asking "why bother?".
Well, not only will it be a welcome distraction, it may provide a boost for both Mr Trump and Mr Netanyahu as they seek re-election.
Mr Netanyahu has managed to secure such a favourable US peace proposal which should serve him well when Israelis go to the polls for the third time in a year, on March 2.
In return, a grateful Mr Netanyahu can help energise the evangelicals that Mr Trump needs if he’s to win in November.