GEOFF BENNETT: Welcome to the "NewsHour."

President Biden this evening said it's his hope that, by next Monday, a deal could be struck to implement a cease-fire in Gaza and start an exchange of Israeli hostages for Palestinian prisoners.

Meantime, Jordan's King Abdullah warned against an Israeli invasion plan for Rafah in Southern Gaza.

AMNA NAWAZ: Rafah is now home to many of Gaza's 2.3 million Palestinians who fled fighting in other parts of the strip.

Following this all is our Nick Schifrin and he joins me now.

So, Nick, let's begin with this hostage deal President Biden says he hopes will be implemented by Monday.

What do we know about that?

NICK SCHIFRIN: U.S. and Israeli officials tell me that they have a new outline of a deal that would stop the war for about six weeks and lead to the release of 35 to 45 hostages.

That includes women, the elderly and the wounded.

Now, one of the obstacles still is female Israeli soldiers, believed to be five of them, whether Hamas will release them.

And there's still no agreement right now as to how many Palestinian prisoners being held by Israel would be released.

Now, the goal of this would be to implement this before Ramadan, which begins around March 11.

Today, on "FOX & Friends," Prime Minister Benjamin Netanyahu reiterated his criticism that he's made multiple times about Hamas' negotiating stance, but also said something he doesn't usually say, that he personally wants a deal.

BENJAMIN NETANYAHU, Israeli Prime Minister: I'm not sure Hamas is there.

They have what I'd call outlandish demands that's like in another orbit, in another planet.

They have to come down to reality.

And I think that, if that's the case, we will be able to have a deal.

We certainly want it.

I want it.

NICK SCHIFRIN: But he also said that he would or is committed to going into Rafah, as he has threatened.

And, as you said, Hamas, some half of Gaza's population, 1.2, 1.3 million people, are in Rafah today, massive tent cities, the city closest to Egypt right there.

The Israeli Defense Forces have presented a plan to evacuate all of those tents that you see, more than a million people, and then assault the city.

But this afternoon, U.S. officials say that they have not received any details of that plan and, frankly, are skeptical that Israel would be able to execute that plan, at least on an Israeli timeline.

AMNA NAWAZ: Nick, I know you have been reporting on the unimaginable conditions on the ground there in Rafah, but the humanitarian concerns extend far beyond that one city, right?

NICK SCHIFRIN: Up and down Gaza, absolutely.

And some of the focus right now is on the quantity of aid that is or is not going into Gaza.

Today, Human Rights Watch accused Israel of not living up to its promises under the International Court of Justice ruling that required Israel to actually deliver as much aid as possible into Gaza.

We also saw an extraordinary scene right there, so many Gazans filling the beach that's on the Mediterranean Sea after Jordan airdropped humanitarian aid.

Jordan has been airdropping aid, but clearly not designed to be in the sea, but that aid is in the sea.

And so many people so desperate for that aid, today, the U.N.

Relief and Works Agency cited a report that a two-month-old baby actually died of hunger and said that one in six children in Northern Gaza are - - quote -- "severely malnourished."

AMNA NAWAZ: Meanwhile, I should ask you about news out of the West Bank.

The Palestinian Authority prime minister resigned today.

What should we understand about that?

NICK SCHIFRIN: Yes, so the U.S. hopes that a hostage deal and a temporary pause, as the U.S. calls it, would lead to a cease-fire, and that that can unlock more regional goals, Gaza governance, how to reconstruct Gaza, and then the larger goal of Israel-Saudi normalization.

And the U.S. hopes that this resignation today is the first step in leading towards some kind of deal over the future of Gaza governance.

So, the prime minister, Mohammad Shtayyeh, resigned.

And Palestinian President Mahmoud Abbas is expected to replace him with Mohammad Mustafa.

Mohammad Mustafa, there he is there, is an economist.

He is close to Abbas.

He has been the chairman of the Palestine Investment Fund.

But, look, the expectations are very low here.

Mustafa is not seen as someone who will change the Palestinian Authority in any fundamental way.

And, of course, Israel has already rejected the Palestinian Authority playing a part in Gaza.

This is really about U.S. credibility and U.S. and its Arab allies being able to coordinate for these larger regional goals that they have.

AMNA NAWAZ: And also another story here in Washington, D.C., I know you have been following related to all of this, on Sunday, there was a U.S. Air Force service member who, in protest of the U.S. policy towards the war in Israel, lit himself on fire outside of the Israeli Embassy.

What should we know about him and what happened?

NICK SCHIFRIN: His is Aaron Bushnell.

He was an active-duty airman.

According to reports, he's 25 from San Antonio, Texas.

The Air Force has confirmed that he died of those wounds last night.

And this is him introducing himself outside the embassy in Washington livestreaming on Twitch, which is a social media platform.

He says - - quote -- "I will no longer be complicit in genocide."

And he called what he was about to do -- quote -- "an extreme act of protest, but compared to what people have been experiencing in Palestine at the hands of their colonizers, it's not extreme at all."

That is the end of the quote there.

He wrote on his LinkedIn page he wanted to be a software engineer and was taking classes in an online university.

The Air Force, as I said, has not confirmed his name, but they have confirmed that he died of his wounds.

Senior defense officials do not believe that he represents some kind of trend inside the military.

But the fact is that this is an extraordinarily rare, very public protest that ended in one airman's death.

AMNA NAWAZ: Nick Schifrin, thank you, as always, for all your reporting.

Appreciate it.

NICK SCHIFRIN: Thank you.