Washington — As the ''grace period'' for young military-draft registrants ends this week, Uncle Sam is wielding both stick and carrot in trying to make this politically controversial program work.
He is giving selective service officials a lot more money to convince young men that a hitch in the armed forces is financially lucrative (with recent pay raises) and just the thing to start a worthwhile civilian profession. But the federal government also is starting to prosecute those who fail to obey the law, pointing out that a federal felony with punishments of five years in prison and a $10,000 fine is hardly the way to begin adulthood.
Government officials and antidraft activists interpret very differently the results of the draft registration effort thus far. The government notes that nearly 90 percent of the 8 million men required to register have done so.
Opponents point out that more than 900,000 have failed to sign up, however, and another million have not notified the selective service of a change of address. The latter is just as much a felony as failure to register.
Reversing his campaign opposition to draft registration, President Reagan in January announced that he would continue the registration program begun in 1980. Selective service officials also said they would extend the ''grace period'' through February and not begin formal prosecutions until this month.
Officials had maintained that it was uncertainty about the President's position which had caused so many young men who turned 18 last year not to sign up within 30 days of their birthday as required. Selective Service System director Thomas Turnage told a congressional subcommittee last week that the compliance rate for those who turned 18 in 1981 had risen from 71 percent to 77 percent since the President's announcement.
''We are optimistic that this trend will continue,'' General Turnage said.
Another view was provided by Jane Midgley, co-chairman of the National Committee Against Registration and the Draft, which this week announced a ''counter-intimidation campaign'' of nationwide protest.
''Hundreds of thousands of young men are not being fooled into registering because they see the registration for what it is: the first step to the reinstatement of conscription,'' Miss Midgley said. She noted the more than 2, 000 standby draft boards being formed around the country, new draft regulations being disseminated, the sharp boost in the selective service budget for advertising and enforcement, and proposed legislation that would reinstitute the draft.
What opponents see as ''intimidation,'' the government sees as effective public relations and law enforcement.
The selective service is seeking a 1982 supplemental appropriation of $1.4 million and a 1983 increase of 17 percent (to $24 million) for such things as radio and television announcements and publicity at high schools and colleges.
Pointing out that registration never dropped below 98 percent of all eligible young men during the Vietnam war, officials expect their new clearly stated policy and advertising effort to pay off with voluntary compliance.
But they also are prepared to enforce the law ''within our existing resources ,'' as Attorney General William French Smith said recently. ''If we can't handle everybody, we'll handle as many as we can,'' Mr. Smith said.
Opponents say this will be a costly exercise that could clog the federal court system if hundreds of thousands still refuse to register. This would not be the case, however, if a proposal by Rep. Les Aspin (D) of Wisconsin is approved on Capitol Hill.
Legislation submitted this week by Representative Aspin, a member of the House Armed Services Committee, reduces failure to register to a misdemeanor with a $200 fine. Under the Aspin proposal, the stiffer felony punishments would go into effect 21 days after any actual draft was reimposed.