The attorney, Dave Swider, said other employees from the Indianapolis janitorial firm will be brought in to perform the work.
"We could do this as long as we need to," Swider said.
Earlier today, Swider said it was uncertain whether the company would replace the striking janitors, subcontract the work or resort to managers' undertaking the cleaning.
The janitors walked off the job to protest what they say is harassment and intimidation by Executive Management Services over their attempt to organize under the Service International Employees Union.
Executive Management Services counters that it has been fair with the workers and has not impeded the organizing attempt.
A union organizer, Rebecca Maran, said about 15 janitors are employed at the building, and that the strike will continue indefinitely.
When asked if other strikes are planned locally, she would only say, "Not that I have public comment on."
Market Tower, which is on Market Street a block east of the Statehouse, is owned by locally based HDG Mansur and managed by Colliers Turley Martin Tucker.
The Class A building has 495,000 square feet on 31 floors.