Kamala Harris is currently tied for second place with John Adams at 29 tie breakers each.
John C. Calhoun is the current record holder at 31 tie breakers.
Harris had two tie breakers on February 28th, one on cloture of a nomination and one on confirmation of a nomination. She had one on March 1st, on confirmation of a nomination.
Her next tie breaker will put her in sole second place.
Her second tie breaker will tie her for the lead.
Her third tie breaker will give her the record.
And she has plenty of time to accrue those three tie breakers.