Washington — President Reagan appears likely to finish his first term in office facing more trouble spots around the world than when he began it. But for the moment that is not necessarily working to the President's disadvantage, at least not here in the United States. Mr. Reagan's Oct. 27 address explaining why US troops are involved in both Lebanon and Grenada has won him political points among Americans.
Polls taken after that address show a high rate of American public approval for the Grenada invasion and a sharp increase in the number of Americans approving the President's handling of the Lebanon problem. Phone calls to the White House are reported to be running overwhelmingly in favor of the President's decision on Grenada.
Administration officials attribute some of the approval of Reagan's handling of these two hottest of the trouble spots to an instinctive rallying around the President in a time of crisis. They recognize that longer-term public support may depend on how quickly the administration can get US troops out of Grenada and whether it can contribute to stabilizing both the Lebanon and Grenada situations. Public support will also obviously depend to a degree on whether further American casualties are incurred in either undertaking.
Congressional critics of President Reagan's action on Grenada charge that the US is now overextended around the world, has violated international law, and is reviving the gunboat diplomacy of earlier years. House Speaker Thomas P. O'Neill Jr. (D) of Massachusetts charged last Friday that Reagan had been looking for an excuse for two years to invade Grenada. Representative O'Neill said the President's action was wrong, unless he can demonstrate that the lives of Americans on Grenada were in danger and that there would have been American hostages.
But O'Neill acknowledged that the American public probably backs Reagan. To the public as a whole, the President has clearly made a persuasive argument for the use of force.
Overseas, the Reagan administration has been criticized for the Grenada action. White House officials are realistic enough not to expect nations outside the Caribbean to endorse the use of American armed force. But they argue that once allied nations are informed of the degree to which Cuba and the Soviet Union had exerted influence in Grenada and moved weapons onto the island, they will show more understanding for the action.
''I believe that as the information we are uncovering reaches the governments and the publics around the world, you will see a great deal more understanding of the necessity to take this action,'' said Otto Reich, the State Department's Coordinator for Public Diplomacy for Latin America and the Caribbean.
''This will translate perhaps not into support in terms of votes at the United Nations but certainly approval . . . for preventing what could have been a much worse situation if it had been allowed to deteriorate,'' Reich said in an interview.
In his Oct. 27 address, President Reagan charged that Grenada was ''a Soviet-Cuban military colony being readied as a major military bastion to export terror and undermine democracy.'' Reagan said that a warehouse captured by US troops contained enough weapons and ammunition to supply ''thousands of terrorists.'' The President also said that the number of Cubans on the island turned out to be much larger than originally expected and that a Cuban ''base'' which was uncovered there made it clear that a ''Cuban occupation'' of the island had been planned. Cuban government officials denied the allegations.
Defense Department officials said later that resistance from the Cubans on the island had been much greater than expected. As of this writing, more than 600 Cubans were reported to have surrendered. Officials said that 16 American servicemen had been killed in the fighting, with 77 wounded and 3 still missing.
But correspondents who visited Grenada four days after the invasion reported that the warehouse on the island which Mr. Reagan spoke of was less impressively stocked than the President said it was. They said that many weapons in the warehouse were from World War II or earlier. And some expert critics remain to be convinced that a Cuban occupation of Grenada was planned.
But when it comes to American public opinion, it looks as though President Reagan's real problem will be Lebanon and not Grenada. Polls conducted by ABC news just before and after the President's address on Lebanon and Grenada on Oct. 27 showed that 55 percent of the public now approve of the way Reagan is handling foreign affairs. Only 38 percent disapprove. A month ago, it was almost the reverse of this: at that point, 42 percent approved and 50 percent disapproved.
According to ABC analysts, however, the jump in approval may be largely based on a positive first reaction to news from Grenada. Many Americans still question the way President Reagan is handling Lebanon. ABC said that only 42 percent of the public approve of Reagan's Lebanon policy, while 50 percent disapprove. Two-thirds of the public say they believe the Marine mission in Lebanon has not been as successful as Reagan has stated. Only a quarter think it has been.
Most Americans say the US should change its troop commitment in Lebanon; 3 in 10 favor sending in more marines. Four in 10 say all should be withdrawn. Reagan has decided not to alter the commitment of 1,600 marines.
Even when it comes to Grenada, there is ambiguity in American attitudes. Many Americans favored the Grenada invasion in part because it showed America can use its power and protect its interests. But the ABC poll showed that a large segment of the public, about 45 percent, believes the US should not use its troops to overthrow communist-controlled governments.
The ABC poll was based on telephone calls made to 250 citizens throughout the nation. ABC cautioned that opinion could shift once President Reagan's speech was subjected to press analysis and to criticism by political opponents.
Some of the critics are charging that President Reagan has unnecessarily increased the US commitment to Lebanon by calling it a ''vital interest'' of the United States while failing to deploy enough troops to match this interest. They argue that Israel did not consider Lebanon vital enough to its interests to keep its troops in the Shouf Mountains near Beirut.
Even within the Reagan administration, some experts are reluctant to view Lebanon as a vital to the US. These same experts are not optimistic about the reconciliation talks among Lebanese factions which are to begin in Geneva this week.