Balanced budget amendment comes closer to foundering with each tick of the House clock

Even if it won in the Senate and has President Reagan and public opinion polls behind it, the amendment to balance the federal budget may not make it to the House floor this session.

It faces a crucial test during the next seven days.

The House Democratic leadership has bottled up the proposed constitutional amendment in committee, and supporters still have not pulled the cork. They are seeking 218 House members to sign a discharge petition forcing the issue to a vote, but they still lack close to 30 names. Moreover, the drive for signatures has flagged during the last two weeks.

The amendment's strongest House ally, Rep. Barber B. Conable Jr. (R) of New York, is reportedly hopeful that he will sign on the needed members, but his office concedes that the deadline is fast approaching. Because of complicated House rules, unless the discharge petition is complete this week, it has almost no practical way of reaching the House floor before the scheduled October adjournment. Currently, items brought up by such a petition can be held up as long as seven legislative days by the Speaker, who in this case is Massachusetts' Thomas P. O'Neill Jr., a staunch foe of the amendment. Moreover, after those seven days, the vote would be permitted only on a second or fourth Monday of a month.

Because of holidays and the Labor Day break, the only realistic date for a vote on the amendment would be Sept. 13. After that, no Monday would be available until late October, when the House will have adjourned so that members can hurry home for elections. Mr. Conable would need to present his completed petition by Aug. 16 at the latest to have any hope of bringing the amendment to a vote before the elections.

Such delay suits the amendment's opponents just fine. Rep. Peter W. Rodino Jr. (D) of New York, chairman of the House Judiciary Committee, has maintained a strategy of slowing action on the proposal. His committee, which has held 14 days of hearings over three years on the amendment, will consider writing its own version. The markup has been scheduled because of strong pressure from colleagues ''to do something,'' reports the Rodino spokesman.

Mr. Rodino has urged House members not to sign the petition. They usually are reluctant to go the discharge route since it short-circuits committee procedures. However, many also face hard political choices with elections less than two months away. The balanced budget is seen as popular among constituents. O'Neill has predicted that if it reaches the floor, it will pass.