BOB SCHIEFFER: I've also got to ask you something, I want to clear this up once and for all. I am told that when you were running for mayor, that there may have been a time or two when you didn't quite get to the event you were supposed to get to, your brother showed up. And if anybody thought it was you, you didn't tell them otherwise. True or false?
JULIAN CASTRO: Well, it was him, but we didn't mean to do it.
REPRESENTATIVE JOAQUIN CASTRO (D-Texas): Yeah.
JULIAN CASTRO: So my political opponent said that I tried to have him go over there for me. But, yeah, he was the one that was there, sure.
BOB SCHIEFFER: He was there--
REPRESENTATIVE JOAQUIN CASTRO: Yeah. Yeah. And we're-- and, Bob, it's interesting, because when I am back home, I'm probably called the Mayor about ten times a day. People think that I'm my brother. But when he's in Washington, and when he was in Austin--
JULIAN CASTRO: So I'm getting payback now--
REPRESENTATIVE JOAQUIN CASTRO: Yeah.
JULIAN CASTRO: --because everybody calls me the Congressman.
BOB SCHIEFFER: Well, I have a-- a friend who served in Congress, and he always tells the story-- his name is Bill Stockley (ph). He always tells the story about one of his constituents called him to complain about her water bill. And his-- her water bill, and he said, "Well, Ma'am, you ought to call the mayor about that." And she said, "Well, I didn't want to go that high." So who-- who outranks who in this family?
JULIAN CASTRO: Well, probably Joaquín now.
REPRESENTATIVE JOAQUIN CASTRO: I say I do.
JULIAN CASTRO: You know, we-- we're proud of him.
REPRESENTATIVE JOAQUIN CASTRO: He's a minute older than I am. So he--
JULIAN CASTRO: Yeah, I always have the privileges of at least being a minute older. But both of us are-- are very, very excited to be working on behalf of the folks from San Antonio. It's an exciting time for our family, of course. And-- and this weekend is-- is fantastic to be a part of it.
BOB SCHIEFFER: Yeah. As a mayor, what's the most important issue to you, immigration reform or gun control?
JULIAN CASTRO: Well, I would say economic competitiveness. Of course, both immigration reform and gun control are long-term issues that are going to be addressed in this term. But for mayors across the country, I mean we hear the stories every day of folks who don't have work, of small businesses that-- that want to grow. And we see the economy picking up like gangbusters now. In San Antonio our unemployment rate has dropped by more than a percentage point in the last nine months. So that's the most important issue. But there are a whole host of issues that are significant and need to be addressed. And that I have no doubt that this guy and all the other folks in Congress will get addressed during the tour.
BOB SCHIEFFER: You know I was struck when you said during the Democratic Convention, you talked about being an education president. But you said you can't be a business President unless you're an education President.
JULIAN CASTRO: Yeah. You know, in San Antonio, we believe that brainpower is the new currency of success in the twenty-first century global economy. And so the only way that America is going to be competitive, that our businesses are going to thrive in the long run when they have to compete against China, against other countries, is that we have a very well-educated population. It's my hope that in this term, President Obama will get to implement the great ideas that he has to link those two, education and economic competitiveness.
BOB SCHIEFFER: If I didn't say so, you're both Democrats, and I probably should add that.
REPRESENTATIVE JOAQUIN CASTRO: Yeah.
JULIAN CASTRO: We are, yeah, sure.
REPRESENTATIVE JOAQUIN CASTRO: That's right.
BOB SCHIEFFER: But Congressman-- you're freshman Congressman.
REPRESENTATIVE JOAQUIN CASTRO: Sure.
BOB SCHIEFFER: What to you is the most important issue?
REPRESENTATIVE JOAQUIN CASTRO: Well, of course, Bob, you know, getting the nation's fiscal situation in order is probably the over-arching issue that we need to-- to deal with. Also, immigration reform, of course, gun safety. But I think right now, at the moment we are in, in our nation, making sure that both parties can come to the table and work and-- and-- and come to agreements in earnest. It's-- it's been a long time since we've been able to do that. So whether it's gun-- gun safety or whether it's immigration, if you can't come and sit in good faith and work things out, then you're going to continue to have a lot of the gridlock that we've had before. I also think that that Speaker Boehner should really consider dropping the Hastert Rule, for example, which I think has been a real-- one of the-- the leading causes of this gridlock that we faced in Congress. So all of these things, and being able to-- make sure that we can-- we can come to agreements and compromise in good faith.
BOB SCHIEFFER: What do you all-- Texas is a very, very Republican state. But some people say the demographics are changing and the demographics alone will make that-- it won't be so-- so Republican next time around.
JULIAN CASTRO: Yeah. In a couple of presidential cycles, you'll be on election night, you'll be announcing that we're calling the thirty-eight electoral votes of Texas for the Democratic nominee for President. It's changing. It's going to become a purple state and then a blue state, because of the demographics, because of the population growth of folks from outside of Texas. And because, unfortunately, the Republican Party has gone so far to the right that they're losing the business community, they're losing the middle.
REPRESENTATIVE JOAQUIN CASTRO: Oh-- no, I think that's right. But it's not going to happen on its own. The demographics are changing, but it's going to take a lot of work from Democrats to lay the infrastructure for change, so we're very busy working on that now.
BOB SCHIEFFER: Well, I want to wish you all the very best.
REPRESENTATIVE JOAQUIN CASTRO: Thank you.
JULIAN CASTRO: Thank you.
BOB SCHIEFFER: Washington could be a wonderful place, Congressman. You'll find out things you didn't think about it, but there will be other things that you'll find out that you-- that are good that you didn't know about. Mister Mayor, congratulations to you.
JULIAN CASTRO: Thank you very much.
BOB SCHIEFFER: And thanks to both of you for being with us this morning.
REPRESENTATIVE JOAQUIN CASTRO: Thank you having us.
BOB SCHIEFFER: We will be back in just a moment.
BOB SCHIEFFER: And that is-- that for-- that's it for us today. Be sure to join us tomorrow for our CBS News coverage of the President's inauguration. Charlie Rose, Norah O'Donnell, and Gayle King will have an expanded edition of CBS THIS MORNING starting at 7 AM Eastern Time. Then I'll join Scott Pelley and the rest of the CBS News team for our Inauguration special report starting at 10 AM Eastern. We'll also have full coverage of the day's events on the CBS EVENING NEWS and CBSNews.com. As for FACE THE NATION, of course, we'll be right here next Sunday.