THE SIZE, alone, of the eligible electorate made this week's House Republican leadership elections more significant than most recent contests for the same offices. Last month's national voting resulted in 33 more GOP members of the House. One would have to go all the way back to 1956 for a caucus in which there were more Republicans choosing a leader than there were this past Monday.

But even with those November victories and the fact that their party is only three weeks away from organizing the Senate, the Republicans in the House remain outnumbered by the Democrats by a margin of about 5 to 4. While a disciplined Republican Senate would be able, at least theoretically, to pass a Republican president's program without relying on Democratic votes, that is not the case in the House. For at least the next two years, Democratic votes will be required to win House passage of President Reagan's bills.

That piece of political reality was argued by supporters of Rep. Robert Michel of Illinois in his successful campaign to succeed the voluntarily retiring Rep. John Rhodes as House minority leader. Mr. Michel won the race over Michigan's Rep. Guy Vander Jagt by a vote of 103 to 87.

Before the voting, Rep. Vander Jagt sent thank-you notes to the 102 Republican colleagues who, mr. Vander Jagt believed, had committed to vote for him. While Mr. Vander Jagt's count may have been off, his reading of leadership contests was quite accurate: "Any leadership race is as personal as you can get," he said. In addition to appeals to old friendships and earlier favors, Mr. Michel's supporters emphasized their man's ability to get those Democratic votes necessary for House passage of the Republican program. "Let's not forget," mr. Michel reminded Republicans, "we're still down 51 votes. Guy Vander Jagt has no experience on the floor and he'd be rebuffed on the other side of the aisle because he's such a political partisan."

Mr. Vander Jagt, a recognized orator and the 1980 convention keynoter, responded with his own "personal" brief: "Inevitably one winds up on 'Face the Nation' or 'Meet the Press.' I think I would be a more forceful spokesman than Bob Michel."

Whether these arguments, or others, prevailed is not known. But what Republicans do seem to understand is that they will have to produce more over the next four years than they have over the past four.

Republicans in Congress, especially in the House, will have the serious responsibility of making policy and law, which is much more difficult than merely making a political record.

One of Rep. Michel's supporters, Rep. Olympia Snowe of Maine, may have spoken for many when she said before the vote: "It's going to be incumbent upon us to produce. I'm going to have to answer to my constituents." That is the mission and the opportunity that await House Republicans and their new leadership team.