The following is a rush transcript of the February 13, 2010, edition of "Fox News Sunday With Chris Wallace." This copy may not be in its final form and may be updated.

CHRIS WALLACE, ANCHOR: I'm Chris Wallace and this is "Fox News Sunday."

(BEGIN VIDEO CLIP)

WALLACE (voice-over): The battle of the budget. Republicans versus Democrats and within the GOP. How much is Congress willing to cut government spending? We'll talk with the chairman of the House Budget Committee, Congressman Paul Ryan.

Then, GOP 2012 presidential hopefuls make their pitch to the conservative faithful, which candidate has the winning message? We'll sit down with a potential contender, Mississippi Governor Haley Barbour. Ryan and Barbour, only on Fox News Sunday.

Plus, Hosni Mubarak steps down as president of Egypt. We'll have a live report from Cairo and we will ask our Sunday panel what it means for U.S. foreign policy.

And our power player of the week provides a place like home for sick children and their families.

All right now on "Fox News Sunday."

(END VIDEO CLIP)

WALLACE: Hello again from Fox News in Washington. We'll talk with our guests shortly. But first, here's the latest on the situation in Egypt.

Ruling military leaders say they are committed to handing over authority to an elected civilian government. They also say the peace treaty with Israel will be honored, and protest leaders announced their demonstrations, which led to President Mubarak's fall, will end. For more, we turn to Fox News' Leland Vittert, who's live in Cairo. Leland.

LELAND VITTERT, FOX NEWS: Hi, Chris. This morning the army issued a couple of statements that is certainly news to the protesters and news they wanted. They suspended the constitution and dissolved the parliament, a couple of key demands they had.

The prime minister here has now said that security is the very number one concern that they have, and to that end the army began clearing out protesters from Tahrir Square. They made a way through this morning for cars to get through so traffic could once again return here.

There are some diehard protesters who say they are not leaving, but there are also protesters who are now coming back in asking that they leave so things can return to normal here. Of course, it is going to be a very long road to recovery economically. Some people have said it is going to take months to get the tourists back here.

This, however, is Sunday, the first day of the workweek, and some businesses were open. There were customers inside one of the pharmacies we were in. So things are beginning to get back to normal. We also have cleaners on the streets trying to fix things up. Of course, there is still a huge army present here on day two of the new Egypt on the street, a number of tanks, armored personnel carriers and heavily armored soldiers. Now the soldiers and the army have promised there will be free and fair elections. The big question, though, is when and how.

This is a country that for 30 years has never had anything that resembled a free or fair election. So there has to be political parties built. There has to be political leaders built and the infrastructure to actually have an election. Chris.

WALLACE: Leland Vittert reporting from Cairo. Leland, thanks for the update, and we'll have more on this with our panel in a few minutes.

Meanwhile, here in Washington, House Republicans have unveiled proposed spending cuts and President Obama is expected to do the same Monday. Joining us now, the GOP's point man in the debate, House Budget Committee Chairman Paul Ryan, who comes to us from his home state of Wisconsin.

Congressman, as we say, President Obama presents his budget for 2012 tomorrow, and he reportedly is going to offer a plan that would cut the deficit, his aides say, by $1 trillion over the next decade. The key feature is a five-year freeze on spending and some considerable tax increases on the wealthy. From what you have heard, what do you think of the president's plan?

REP. PAUL RYAN, R-WIS.: It sounds like the similar budgets that he has been giving us the last couple of years. Last year, he gave us a $2 trillion tax increase. He got $700 billion of those tax increases enacted, mostly through his healthcare law.

It looks like he is coming back for another, I don't know, $1.3 trillion in tax increases.

This discretionary freeze is off of an extremely high base. They just blew spending out the gates in the last two years. A 24-percent increase in domestic discretionary spending. When you throw stimulus on top, it was an 84 percent increase, and he wants to freeze for a few years off those high levels. It is less than 1 percent of spending over the next ten years.

We'll see the details of this budget tomorrow, but it looks like to me that it is going to be very small on spending discipline and a lot of new spending so-called investments.

Look, the president is elected to lead and to face the country's biggest challenges. The country's biggest challenge domestically speaking, no doubt about it, is a debt crisis, and I'm really hoping that he is going to give us a budget that tackles this debt crisis. And if it is what these early press reports show, it shows that he is abdicating leadership on that point. I'm hoping that is not the case, that we can get this debt going down. But it looks like the debt is going to continue rising under that budget.

WALLACE: Well, if it is as it has been reported, and there is every reason to believe it -- these are leaks from the White House -- is this budget, which has some spending increases for infrastructure and education and research, is this budget, the president's budget dead on arrival?

RYAN: Well, look, I don't like to say that until I actually see the budget. So, I wish I could give you a clean, clear answer. But again, I want to look at the actual budget. We will get this tomorrow. We will pore through it line by line very quickly. We know how to analyze these things pretty quickly, and then we will give you an answer to that tomorrow.

But, look, if he is talking about coming and having new spending, so-called investments, that is not where we are going. The great debate we are having in Congress now, which is refreshing, is we are debating how much to cut spending, not how much to increase spending. And these early press reports are showing us that he wants paltry savings on the one hand and a lot of new spending on the other hand.

Borrowing and spending is not the way to prosperity. Today's deficits means tomorrow's tax increases, and that costs jobs. So all this borrowing and spending doesn't work. Didn't work on the stimulus, and it will cost us jobs. We need to cut spending so we can get taxes and interest rates low so businesses can plan and hire people.

WALLACE: But, Congressman, a number of business leaders, including Tom Donohue, the head of the Chamber of Commerce, say that the economy needs some -- not a net -- but some new investments. He talks particularly about infrastructure, to create jobs. There are a number of independent economists out there that say if you have too many cuts too quickly when the economy is so weak, that that is going to hurt the recovery.

Let me ask you specifically, and we are going to get to the details of your budget in a minute, but how do all of these spending cuts create jobs in the short-term, in the next year?

RYAN: Ben Bernanke came to our committee a few days ago and said if you guys put in place a real plan to get the deficit under control, that will help the economy now, because that sends the signals to the markets, to the small businessmen and women of America that my taxes aren't going to have to pay for all this borrowing, that interest rates are going to be low.

So getting spending under control today gives confidence for tomorrow, and that leads to more hiring and job creation.

Look, I am not worried about Washington cutting too much spending too fast. I mean, the kinds of spending cuts we're talking about just right now are $100 billion out of a $3.7 trillion budget.

So I am not concerned about that. What I'm concerned about is endless borrowing, which is going to compromise our economy not only today but in the future. Because we know the decisions we make right now really dramatically impact us in the future, and the debt is literally getting out of our control.

And if we bring a budget that continues to send the debt out of control, that today hurts the economy. So spending cuts, yes, in fact help us with jobs today.

WALLACE: All right, Congressman, this gets a little confusing. The president is going to be offering a budget for the next budget year that starts in October, 2012.

RYAN: Right.

WALLACE: This week you guys, the House Republicans, are going to offer some cuts in the current budget, the 2011 fiscal budget, for the next seven months that are still left in it.