Washington — President Reagan proclaims that the defeat of the balanced budget amendment will reverberate in the voting booths next month and urges the public ''to count heads and take names.''
House Republicans are saying, after the vote Friday, that they already are prepared to publicize the message that Democrats have thwarted the will of the American people. ''It was not defeated by Republicans,'' said Rep. Barber B. Conable Jr. (R) of New York, the amendment's chief sponsor.
''It'll shift the whole tenor of the debate,'' according to Republican Whip Trent Lott of Mississippi.
Meanwhile, to House Speaker Thomas P. (Tip) O'Neill Jr. (D) of Massachusetts, rejection of the constitutional amendment is no more than a ''one day story'' that will soon be superseded by the economy.
''I think it's over,'' said Majority Leader Jim Wright (D) of Texas, who denied that his party will be injured by the issue. ''Most of the American people realize that the Constitution is a sacred document.''
Almost no one questions the overwhelming support of public opinion for the idea of balancing the budget. But the idea of unseating Congress members who oppose the constitutional amendment is far from certain as the fall election campaign moves down the home stretch.
In fact, about the only fixed fact about the balanced budget amendment issue is that it became one of the liveliest political footballs of the congressional session.
Events began with a rare spectacle July 19 - the President led a rally on the steps of the Capitol to push for the amendment. Soon after, the Senate passed the amendment by the required two-thirds majority.
Then opponents began a series of defensive actions in the House. They locked the measure in committee. The only way to force a vote was to gather the required 218 House signatures for a discharge petition. Since such petitions are almost never successful, the matter seemed hopelessly stuck as adjournment neared.
But a behind-the-scenes struggle ensued, with each side putting on heavy pressure. Representative Lott complained that his side ''couldn't even write down the names on the discharge petition,'' which is kept in the House chamber. ''We had to send four or five people to memorize them,'' he said.
As the petition neared the required number of signatures, the Democratic leadership persuaded some members to remove their names. So amendment backers and Republicans devised a new strategy. They worked intensely to gather the last 13 needed. Once they had them, the group marched en masse onto the House floor, signed the petition, and put it over the top. So organized was the ''coup'' that Vice-President George Bush was on hand to greet the 13 in a Capitol meeting room.
Apparently outflanked, the Democrats responded with a surprise of their own. They decided to bring the amendment to a vote immediately, giving the President less time to make appeals and, they hoped, snuffing out the balanced budget amendment as a political issue.
When the amendment came to the floor last Friday, the opponents inserted their voting cards so fast that the measure was defeated after less than two minutes.
However, the movement for a balanced budget amendment still has some life. There are still 31 states that have called for a constitutional convention to write such an amendment. That effort has flagged in recent years, although the National Taxpayers Union is now expected to step up its drive for a convention.
The issue is likely to reappear on Capitol Hill, as well. Rep. Conable says he plans to reintroduce it next session.