At the national convention of the Palmer Drug Abuse Program, First Lady Nancy Reagan and Republican Texas Gov. William P. Clements displayed one friendly difference in their respective crusades against drug abuse today.

"I don't really care where peddlers, dealers or pushers go," Clements said he told Tennesee's Gov. Lamar Alexander not long ago. "I just want them to get the hell out of Texas."

In her keynote address after Clements' remarks, Mrs. Reagan said she thought the governor was "wonderful" in what he's done to rid drug abuse in Texas. "But I want to see drugs out of all the states," she said.

Both views illustrated the Reagan administration's position on eradicating illegal drugs throughout the country. President Reagan recently raised the battle flag by announcing the formation of a drug task force and signing an executive order elevating Carlton Turner, his senior adviser for drug policy, to the new position of director of the White House Drug Abuse Policy Office.

Turner is coordinating efforts by federal health and law enforcement agencies but will leave the ultimate solutions up to local authorities.

"Clements' success in chasing drugs out of Texas shows what local people can do and we're asking other states to be as forceful in programs they devise," Turner said today.

Clements told the conference that he will bring the issue, at President Reagan's request, before the National Governor's Conference next week in Oklahoma. He said he hoped the governors would attempt to mobilize parents, teachers, service clubs, law enforcement agencies and others to stamp "this cancer out of our society."

About 1,000 parents and youths involved in the Palmer treatment program also heard former Dallas Cowboy quarterback Roger Staubach, the third member of the inspirational trio, urging them to remain dedicated, stick to their priorities and persevere toward their common goal.

"We love you Roger," the T-shirt and blue-jean clad youths shouted, as Staubach wound up his talk. Then they gave Mrs. Reagan an even more rousing ovation.

"Gov. Clements and Roger Staubach make me think of how similar politics and football are," said the first lady. "But as my husband says, at least in football you get to wear a helmet."

Mrs. Reagan's approach on drug abuse is to remain impartial about the method of treatment, though she advocates parental involvement. She became interested in the Palmer Program after hearing actress Carol Burnett describe what it had done for her daughter.

"I know you lost a lot as a result of drugs--friends, family and maybe your own identity for a while," Mrs. Reagan told the crowd.

"But I can't tell you how proud I am that you struggled so hard. One thing you gained without even trying is credibility. When you speak about drugs and alcohol now, other young people listen and trust you."

Later, sitting among the youths, she answered questions posed by them about why she had come, her views on legalizing marijuana, what Congress thinks about the drug situation and whether there should be stricter penalities against government officials and law enforcement officers who use drugs.

"You can't separate political people from anybody else," she replied.

One young woman said she always wondered whether Mrs. Reagan was "really human." And seemed surprised that "you're just a human being like everybody else."

Mrs. Reagan laughed at that and at another question asking how it felt to be the president's wife.

"As long as the president is Ronald Reagan it's great," she said.

The session proved to be an emotional one as Mrs. Reagan was hugged and kissed by two youngsters presenting her with mementos of the occasion. Her chief of staff, James Rosebush, said later that the first lady "loved it."

"I thought it was a love feast. They seemed to be looking to her as a symbol," Rosebush said.

Lisa Shain, 19, of Corpus Christi, said she has been "straight" for three months after seven months in the program and after five years of using "every kind of prescription and street drug."

"Instead of feeling 19 when I went into the program I felt like I was 90, a very old person and very exhausted," Shain said.

She called Mrs. Reagan's appearance here a big boost.

Donna Nimmo of the Dallas suburb of Garland, parent of a 16-year-old enrolled in the program, said she valued Nancy Reagan's visit because of the credibility it gives to the work.

Another parent, Sid Armistead, also of Garland, and also with a 16-year-old daughter in the program, said he thought the first lady would be more effective if she were to get involved on a day-to-day basis in a treatment program such as Palmer's.

But if Mrs. Reagan had any doubts herself about her effectiveness in her self-chosen role, she doesn't any longer.

"I'm constantly amazed at how many people want to talk to me about it," she said later. Mrs. Reagan flew back to Washington today after winding up a two-day trip of looking at drug- and alcohol-abuse treatment programs, which also took her to Iowa on Thursday.