Chat with Chris Wallace . . . and a Bill Moyers report

''I'm so happy that every once in a while I say to myself, 'It just can't stay this good!' Maybe that tells you something about my upbringing,'' says NBC newsman Chris Wallace.

As a matter of fact, this co-anchor of NBC's ''Today'' (weekdays, 7-9 a.m.) had a very unusual upbringing. His father is Mike Wallace. When he was eight his mother remarried and his stepfather is Bill Leonard. Both men have played an important part in CBS News, and in Chris's life.

While being interviewed in Bryant Gumbel's borrowed ''Today'' office in the Rockefeller Center headquarters here of NBC (Chris is the Washington end of the tri-anchor, with Bryant Gumbel and Jane Pauley operating from New York), he is asked if his fathers gave him professional advice while he was in college.

''One of my fathers--and I can't remember which one it was--advised me to go into newspapers first. So I took a job at the Boston Globe after I finished Harvard. From there I went into TV, although never at CBS where my fathers worked. I was very careful about that--it was important to me not to seem to be trading in on my family connections. That newspaper experience has always stood me in good stead. You learn to write better and report more thoroughly. You learn to put one sentence after another in logical form.''

Chris looks like the brightest kid in the class. However, what comes across is self-assurance mixed with humility and carefully researched knowledge. Since his Republican convention coup, when he was first with the word that Ford would not be Reagan's running mate, newsmen and the public have watched him mature as a TV reporter.

''Today'' has held its own since he arrived a few months ago and seems on the verge of wresting back control from ABC's ''Good Morning America.''

Chris is concerned about the ratings demands being made on TV newsmen. ''There was a time on TV when all you had to do was be good. Now you have to be good and have a 30 (percent) share (of the sets in use). Not that there is anything wrong with being popular--after all, we are a mass medium concerned with reaching as many people as possible. But there are now certain pressures on newsmen that aren't always healthy pressures--to look good and to be entertaining. And although '60 Minutes' has been a huge success, where is it written in stone that each network has to have a news magazine show?'' (Chris served for a time on NBC's magazine show, which has just been canceled.)

Have his family connections been a plus or a minus in his professional life? And have they influenced his style?

''I gotta tell ya,'' he starts, sounding very much like his father Mike, ''if I've been influenced I am unaware of it. I certainly do not pattern myself after them, although maybe there are similarities. It's probably just a kind of osmosis between father and son. But certainly I was lucky to grow up with two Dads involved in quality news. I learned a lot from both of them just by listening.''

Does Chris have much professional contact with Mike?

''Well, we had dinner together last night and we talk to each other on the phone all the time. We criticize each other's work--he calls me up and tells me if he feels I've done something good and I do the same for him. I value his judgment. In this business a lot of people play games and it's nice to have two people like my dads whom I can depend upon for the truth.''

Dad Mike Wallace told the Monitor: ''Chris is a good reporter, a quick but thorough study, and he's in an ideal job which gives him a chance to do a wide variety of things. He's better educated than I ever was. We are not just father and son -- we are good friends. He's one of my favorite critics. . . . What a kick it is to get up in the morning and watch him -- even if it isn't my own network.''

Chris believes that a totally hard-news morning news show may never make it on TV. ''CBS has had a good news show on in the morning for more than 20 years. People don't really want to watch so much hard news at that hour.''

''Not that our show is that soft. If you look back at early 'Today' shows you find that there was a lot of show-biz involved. There were actresses as co-hosts then. And J. Fred Muggs. I feel we are now doing just the right mix of news and features.'' 'People Like Us'

Is President Reagan's new budget asking the wrong people to sacrifice?

That's the major question that recurs again and again in Bill Moyers's incisive CBS Report: ''People Like Us'' (CBS, Wednesday, 8-9 p.m.). It is a question which is never answered in words -- only in a series of picture portraits by cinematographer Tom Spain and the words of Bill Moyers.

Mr. Moyers, often called ''the conscience of American television,'' once again proves that his concern for the little people, the undefended minority, remains steadfast whether he is on PBS or CBS.

''People Like Us'' focuses on the poor people ''who have slipped through the safety net . . . the truly needy people whom the President said would not be hurt.'' Moyers chooses just a few of the helpless poor and lets us look in on their appalling situations, forcing the viewer to recognize the danger of harming the truly needy as we attempt to eliminate the welfare cheaters and cut down on poverty programs in general.

He points out that the government lost $95 billion in revenues last year because some taxpayers underreported their incomes. According to Moyers, that is seven times the total welfare budget. So, where is the clampdown needed?

What is unforgettable about this program are the intimate portraits it paints of several impoverished families who are suffering because of the new budget cuts in poverty programs. Moyers comments to a priest in charge of a Milwaukee church food center:

''President Reagan would be very proud of you because you are trying to run a voluntary program here with no government money. And I think in a sense you're proving what the President said, that we can invent ways to solve our social problems without government intervention.''

The response he elicits from Father Gliko: ''What the President says in a way is true . . . but it's unfair to put any poor person in the precarious situation of having to depend upon the generous whims of the wealthy.''

Concludes Moyers: ''There's no question but that the federal programs which help the poor are riddled with waste and fraud. So are programs that help the middle classes. So are subsidies to corporations. So are the billions spent on the military-industrial complex. But the President and the Congress have chosen not to offend the rich, the powerful, the organized. It is easier to take on the weak. . . .''

''People Like Us,'' produced and directed by Judy Towers Reemtsma, should in the long run make you feel proud of the people who are trying to do something about it and hopeful that they will be able to make others aware of the desperation of the poor. Once again Bill Moyers has pointed the finger of conscience at a malaise in our society through a superb public-service documentary -- and once again he has forced viewers to think about doing something to change it.