A constitutional amendment barring school busing for racial balance has only a fair chance of passing the House, its author, Rep. Ronald M. Mottl (D-Ohio), admitted yesterday.

But he added that he hopes to generate enough public pressure by the scheduled July 24 House vote on the amendment to get the two-thirds votes necessary to pass it.

"If people let their feelings be known to House members over the July 4 recess, the chances are good," Mottl said.

Mottl caught the Democratic leadership off guard late Wednesday night when he suddenly got a last burst of signatures to attain a House majority of 218 on a discharge petition. The rarely successful procedural device automatically takes the bill in question away from the committee with jurisdiction over it and requires a House vote on the measure.

Mottl, who comes from the Cleveland area, where court-ordered busing is in effect, has been fighting for the constitutional ban on busing since he went to Congress in 1975. But the Democratic leadership has bottled up the busing amendment in the Judiciary Committee, refusing even to hold hearings on it.

"Court-ordered busing . . . causes white flight to the suburbs. It causes resegregation of city schools . . . and is a waste of tax dollars . . . and of our precious gasoline supplies," Mottl said, adding that there was also no evidence that it improved the quality of education.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) predicted yesterday that the busing amendment would not get the two-thirds vote necessary to pass the House, but he was less sure of that Wednesday night, when he admitted that it would be hard, politically, to vote against the amendment.

Both Mottl and O'Neill agree that it would be very difficult to pass the amendment in the Senate.

Mottl came close to getting the required number of 218 last year.He got up to 203, but every time he got a few more signatures the Democratic leadership persuaded some members to take their names off the list.

Unlike other petitions, a discharge petition is held at a desk in the well of the House, and a member must formally go up and ask to sign it.

"Many members don't want to so visibly offend a committee chairman or the leadership by doing that," said Rep. L. A. (Skip) Bafalis (R-Fla.), who helped Mottl obtain the last signatures for the discharge petition.

This time Mottl and Bafalis changed their strategy. After obtaining 209 votes, they asked the last nine signers to await a prearranged signal and go to the desk together, so there would be no opportunity to take names off the list. Once the 218 figure is reached no names can be withdrawn.

Even so, the leadership convinced two members to drop off the list early Wednesday. And when the prearranged time came to go to the desk, around midnight, in the midst of a debate on a Labor-HEW appropriations bill, one member, Rep. John T. Myers (R-Ind.) fled from the floor to make a telephone call.

He was hotly pursued by Minority Leader John J. Rhodes (R-Ariz.), who argued with him to get off the phone and keep his commitment to sign the petition. But a replacement was found for Myers, and his signature was not needed.

Signers of the petition included 131 of the House's 159 Republicans and 87 of the House's 276 Democrats. Democratic signers came mostly from big city areas where court-ordered busing is in effect, such as Boston, Louisville, St. Louis, Detroit and Cleveland.

Mottl's amendment would prohibit compelling a student to attend a public school other than the one in the school district nearest his or her residence. Mottl denied that his amendment would end integration of schools, and said he favored voluntray busing and "magnet" schools as an alternative.