WE IN THE PRESS have been sensitized for years now to the fact that many conservatives believe that there is a liberal bias in the media. We understand that while few really think that many of us actually are subversives, they do barbor deep suspicions that -- at the least -- we have more than our share of irresponsible opportunists who are a burden to democracy and weaken the national security.

A number of recent polls are even more unsettling to reporters. They appear to reflect public support for everything from the military excluding the media from the Grenada operation to libel suits against major news organizations. And they have reinforced the concern of many of us in the news business that there is a serious problem with Americans supporting or even understanding a free press.

It wasn't always like this. My recollection of 25 years ago, when I started out in the newspaper business, is that most of my friends and relatives thought I was working in a conservative institution, albeit a raffish and disreputable one.

But a number of factors -- including the deep national divisions over the Vietnam war and Watergate, the emergence of network television as a national institution and the rise in journalists' educational levels -- have changed the public's perception of us over the last two decades.

Whatever the reason, we tend to worry about the First Amendment and maybe feel just a little bit sorry for ourselves. A new and provocative study of public attitudes toward the media by the Times Mirror Co. suggests, however, that our biggest mistake may be our misunderstanding of what the American people think of us.

A national sample of more than 2,000 who were interviewed and re-interviewed in depth by the Gallup Poll indicates that the citizenry is much more supportive of the media in general and news organizations and individual journalists in particular than we realize. It also shows that the public is more discriminating in its attitudes toward the press than many of us think and that its opinions cut across ideological, social and economic lines much more than we thought.

The public thinks we are too much influenced by and dependent upon government, special interests and other institutions we cover and by the need to attract a mass audience. They also think we are often biased -- liberally biased more often than not -- and unwilling to admit error.

Thus, the major fault the public finds with us, according to this study, is that these shortcomings get in the way of our proper function of acting as a "watchdog" on the government and other powerful institutions. One of the most striking findings of the study is the high value most people place on this function and their criticism of our weakness in performing it.

Only a third of the respondents are aware that freedom of the press is guaranteed by the First Amendment. But in nearly every question involving government control or interference in disseminating the news, a majority -- mostly two-thirds or more -- support the media against the government.

The percentage of those who believe that "press criticism keeps political leaders from doing what should not be done" ranges from a low of 61 percent (non-whites) to 75 percent (college graduates). This approval cuts across every age, educational, occupational and political group -- "strong conservatives" agree with it by 66 percent, "strong liberals" by 75 percent.

When asked about the controversial publication of the "Pentagon Papers," the documents outlining the U.S. involvement in Vietnam, a whopping 66 percent approved publication while only 21 percent were opposed. Nearly 80 percent believe that a reporter sometimes "should be allowed to keep his source confidential if that is the only way he can get his information."

But when the conflict is between the press and individual rights, the press loses every time.

Forty-nine believe that the growing number of libel suits is a good thing because they help keep the press under control and from becoming "less responsible" in dealing with individuals.

Only 23 percent define freedom of the press as the freedom to "report what it chooses." Sixty-one percent define it as the "public right to hear all points of view."

All of this is a remarkably discriminating view of the media, even where contradictory.

The study turned up other surprises for journalists. One is that for all the criticism we feel, people really don't think or talk about us much of the time. Only about 20 percent talk about us some of the time, which ranks us in interest behind, in this order, political leaders, entertainers, doctors, athletes, lawyers, clergymen and businessmen. The only group that stimulates less conversation than journalists is scientists.

Another is that for all the criticism and lack of talk about us, people like us to a remarkable degree.

About 70 percent are generally favorably disposed toward the media. Only about 15 percent find little or nothing good about us. Ten percent of these feel alienated from every major institution and the other five are our informed, vociferous, predominantly conservative and Republican critics -- who question our morality, patriotism, competence, honesty and independence.

But most people like us because, for all the criticism, they think we're competent and believable -- and they like the news. They like being informed. One of the most interesting findings is that during the TWA hostage crisis, which brought our critics out in full voice, the public's positive attitudes about us increased.

What conclusions can we draw from all this?

One is that we may be better off in terms of public support than most of us realize but that we still have a long way to go. Another is that the best way to counter our critics is simply to do what we pride ourselves in most -- being fair, competent, accurate, thorough, independent and tough. And to never forget that we can always do the job better.