Trying to harvest farm vote for the GOP

''The question still is whether we can govern in the next two years,'' an administration official says.

As the fall campaign nears its end, President Reagan's objective remains what it was at the beginning: to ward off a recession-related defeat that could result, this same official concedes, ''in a stalemate government until the end of the President's first term.''

The immediate question is whether Mr. Reagan's ''stay the course'' theme is working - whether the voters who elected him will stick with him and give him enough Republicans in Congress to continue his program of cutting government's size.

The President's people say they are well aware of polls showing that voters appear ready to increase the Democrats' margin in the House by a sizable amount. But they point out that these same polls called the Reagan-Carter election extremely close, right up to the time of the 1980 election; their findings never reflected the Reagan landslide that was in the making.

Indeed, there are signs along the campaign trail that the President, through several concessions to farmers that include increasing grain sales to the Soviet Union, is taking some of the steam out of the incipient farm revolt.

Several thousand farmers waited for hours, braving a rather nasty day, to hear the President at Chapin, Ill. They weren't there to air their grievances. If there was any anger, it was muffled. It was a happy throng, eager to see the President.

New reports from the farm belt indicate that farmers are supporting Reagan. Most of them have been voting Republican - they and their fathers and ancestors - going back to Lincoln. They seldom vote Democratic. When dissatisfied, they are more likely not to vote at all, thus helping the Democrats win.

But now, with the growing feeling that the President is doing something to ease their lot, Republican farmers seem bent on supporting their party and their President.

Actually, new Reagan polling indicates a resurgence of support for the President among Republicans everywhere. In percentage it has dipped a bit in recent weeks but is now up again in the mid-to-high 70s.

The chief thrust of the Reagan campaign really is directed at making sure that these Republicans get out and vote.

But it would be an exaggeration to say that there is more than just a cautious, relative optimism in the Reagan ranks. The Reagan people are heartened by the thousands who came out to hail the President at an evening rally in Peoria. But they were also mindful of the several hundred demonstrators outside the civic auditorium and of the several thousand workers who met a few days ago in Peoria to complain vociferously about widespread unemployment and to blame the President for their plight.

The mood among many blue-collar voters who backed Reagan two years ago can only be described as ugly. They seem ready to send a message to the President - and it isn't one he would like.

Political observers all around the US now are taking new readings on the campaign. And they are becoming more cautious in their estimates of the size of the Democratic victories in the House that appear imminent - and which would be historically a ''normal'' expectation in the first midterm election after the election of the President.

And a reporter with the President soon senses that this is a chief executive who definitely is not in trouble. In general, the public at rallies and along motorcade routes is friendly. The signs held high are generally warm in their greeting. For the most part, voters still like Mr. Reagan and want him to succeed. And there still is a surprising amount of patience among voters for this President and his program. There is an ''I like Ron'' feeling in the air reminiscent of the ''I like Ike'' mood along the campaign trail in the 1950s.

How much of this tolerance, even affection, for the President will be reflected in the fall congressional elections? The President's advisers don't know. But the reason Reagan is traversing the country in these waning days of the campaign is because of a hope that he can translate his popularity into votes for Republican candidates.