RAY SUAREZ: Now two assessments of the speeches and what's next from Ghaith Al-Omari, a former adviser to President Abbas, now executive director of the American Task Force on Palestine, and David Makovsky, director of the Project on the Middle East Peace Process at the Washington Institute for Near East Policy and former executive editor of The Jerusalem Post.

Well, Ghaith, earlier this week, the Obama administration tried to convince Mahmoud Abbas not to go ahead with the bid. Obviously, they didn't succeed. But why now and why this?

GHAITH AL-OMARI, American Task Force on Palestine: Yes, now because the two factors.

One is a sense of frustration. And I think Abbas expressed it today in his speech, a feeling that the negotiations were going nowhere, a feeling that settlements were being built in a way that will undermine the two-state solution.

Add to it the second factor, which is the Arab spring, the movement among the peoples of the Arab world demanding action from their governments, I think Abbas felt that he was compelled to do something, to show that he is not simply sitting there, but he is moving the ball forward.

RAY SUAREZ: David, an hour later, Prime Minister Netanyahu took to the lectern and delivered a tough speech. He has said that things will go badly on the ground in that area once that statehood bid is made. What has it changed for Israel?

DAVID MAKOVSKY, Washington Institute For Near East Policy: Look, I think he was trying to tell the world that the way to statehood runs through peace, and it cannot be divorced from it, and that anything done in the U.N. is not just a purely symbolic move, but could have real implications in making peacemaking more difficult.

And given that these people live on top of each other, almost, too much history, too little geography, these are the people that have to live with the results, so they have to actually sit together and solve their problems. And then they go to the U.N. and announce the two-state solution.

RAY SUAREZ: But what does it change? The document has been filled out, handed over with much fanfare. What does it change in Israel?

DAVID MAKOVSKY: Look, it doesn't change much. If it focuses the effort of the Quartet, the U.S., European Union, as you said in the setup piece, to call for renewed talks -- this is something the U.S. and Israel have wanted for a long time.

So by weighing in this afternoon after the two speeches, the international community is basically saying, let's cut the symbolism. Let's go straight to talks now. It will change things only in Israel if it leads to violence as a result of all this, if the dynamics are unleashed that cannot be controlled.

I don't think either Abbas or Netanyahu want this at all, so I think the main arena now with the international community weighing in is a return to talks.

RAY SUAREZ: The Abu Mazen speech got a rapturous applause among the members of the General Assembly. Now that this has been done, what does it change for the Palestinians?

GHAITH AL-OMARI: One thing that changes for Abbas himself, his popularity internally has increased, which means that his margin of maneuver has increased.

Now, no Palestinian thinks, definitely Abbas doesn't think that going to the U.N. will get you a state on the ground, but he feels that this might strengthen his negotiating position. But at the end of the day, he knows that you have to go back to negotiations. He talked about this in his speech.

And, indeed, as David said, the Quartet now, we will see very frank diplomacy over the next days and weeks to try to create a formula for both sides to get together. But at the end of the day, I think Abbas feels that he raised the temperature, increased the pressure, and creating more leverage for himself.

RAY SUAREZ: But, Ghaith, it's been widely said by friends of both sides that you need two sides to talk. This doesn't dismantle a single settlement...

GHAITH AL-OMARI: Absolutely.

RAY SUAREZ: ... doesn't take down a yard of the barrier wall. Why was it so important, if it antagonizes the people you have to talk with?

GHAITH AL-OMARI: Again, you look at this as part of a process.

While, on the one hand, Abbas doesn't really trust Netanyahu -- and this goes both ways -- he looks at it as a way of increasing his leverage. But at the end of the day, and I think it's worth pointing out that as this systematic wrangling goes on, there are things happening on the ground that we can build on.

David talked about the risk of violence. And this is a fear shared by both communities. Yet we have security cooperation that is ongoing. Let's make sure this continues. The Palestinians have been working on building institutions to increase governmental -- governance, increase -- improve the economy. Let's make sure this goes on, because that's where progress will really happy, until diplomats get to the right place and until the politics of both sides and in this country allow us to go back to a meaningful negotiation.

RAY SUAREZ: David, along with a long litany of Palestinian grievances, President Abbas' speech also included several messages to Israel, assuring it of a peaceful future and of security guarantees that can be durable.

Was this important for Israelis to hear from the U.N. today?

DAVID MAKOVSKY: I think, frankly, Ray, it was lost.

I mean, I think the overall impression -- I'm glad, by the way, Abbas spoke in Arabic. That's important. But I think it was basically assuring his own people, this is the Palestinian narrative that I'm bringing to the world.

That was, I think, certainly the tone that was heard. I don't think it was much more extending a hand: Here's how we can renew talks. I don't think that that really carried over. He didn't prepare his people for compromises or be seen as telling the Israelis, here, we could build this two-state solution.

It was more bringing the Palestinian narrative to the world. I kind of expected it. And you could tell by the reaction in Ramallah that that is what they heard, and that was well-received.

RAY SUAREZ: Well, what do the Israelis need to hear from the Palestinians now to at least have an opening to talks? The Quartet has called for new talks today and other prominent members of the U.N.

DAVID MAKOVSKY: I think you need -- what they would want to hear is Abbas say something like this: We understand your fears. You have to understand ours. Your fears are that you got out of Gaza and Lebanon, and you got rockets. And we know, with the Arab spring, Egypt and Jordan are much more shakier now. We understand that these security arrangements have to be ironclad for you, that the peace has to be every bit as strong as the land is tangible that we expect to gain.

So I think he has got to focus much more on the security side, because it's clear on the land side, he had already heard from President Obama. Netanyahu kind of hinted it today, that it will be based on the '67 lines, plus land swaps. That means land exchanges. So both sides have to be assured going forward.

RAY SUAREZ: Given the way things stand at the close of today, is the Palestinian delegation inclined to give Israel what it needs to reopen talks?

GHAITH AL-OMARI: As David mentioned, today, both leaders spoke to their constituencies, and that's the only way to understand how Bibi Netanyahu talked about -- called the U.N. a house of lies in the U.N.

But both sides I think now go back home feeling more strengthened, feeling more energized, feeling that they have a more secure base. I think if we play the diplomacy right, we can build on the sense of triumph that both sides have to bring them together to talks.

At the end of the day, what the Palestinians need to hear from the Israelis is clarity, in terms of what are the bases for the negotiations, to ensure that it will be on '67 with a mutual swap, as President Obama called for, and to hear something about settlements. Once we have these basic issues taken into account, once both sides hear from each side what they need on hear, I think the space is there for a negotiation.

Keep in mind that both the Israelis and the Palestinians, the publics I mean, as borne out by all of the polls that we have been hearing about consistently for years, 70 percent of both communities want a two-state solution. So what we need is empowered leaders who will be able to deliver that. And I hope what happened today will lead to the leaders feeling more secure and able to make the necessary concessions.

RAY SUAREZ: David, before we let you go...

DAVID MAKOVSKY: Ray, can I just say that -- can I just echo that thought?

RAY SUAREZ: Sure.

DAVID MAKOVSKY: I think, if the net effect of today was that both sides giving muscular speeches to their publics gives them the political cover to pivot, to talk as empowered leaders, then maybe something good came out of this. If they don't make the pivot, then I fear that this could be a slippery slope downwards towards confrontation.

RAY SUAREZ: And when you say make the pivot, are we talking about a few weeks, a few months? Is this a moment that has to be captured quickly?

DAVID MAKOVSKY: Well, in the Middle East, the popularity doesn't last too long. And I think they need to pivot pretty soon.

And that's why it was very important what the quartet did this afternoon and called for the direct talks. This has been in the works since May. And they just released a statement, not coincidentally, after the speeches of the two leaders today.

RAY SUAREZ: David Makovsky, Ghaith Al-Omari, gentlemen, thank you both.

GHAITH AL-OMARI: Thank you.

DAVID MAKOVSKY: Thank you. Thank you, Ray.