"I don't sense the support of an override in the Senate among the membership," Mr. Cagle, who presides over the Senate, told reporters.
His remarks come a day after Senate President Pro Tem Eric Johnson said he would not vote to override the veto as long as the extra revenues are used to restock Georgia's rainy day fund.
That sets the Senate on what could be a collision course with the House, where leaders have vowed to again challenge Mr. Perdue to salvage their $142 million property tax refund.
Late last week, Mr. Perdue vetoed the midyear spending plan, which contained a House-sponsored refund for Georgia homeowners. Mr. Perdue said the spending plan did not fund critical state programs.
The House voted overwhelmingly last week to override the veto, but the Senate refused to take up the matter. Mr. Cagle said the House vote was invalid because Mr. Perdue had not transmitted the veto back to the Legislature, as the constitution requires.
The impasse has set the stage for a special session to rework the budget, which contains badly needed funds for public defenders and for the state's PeachCare health insurance program for poor children. Mr. Perdue has said he will announce the dates for a special session this week. Once he transmits the veto to the Legislature, the House could vote again to override.
Mr. Cagle said leaders were at the table but there was no agreement yet on how to break the budget logjam.
"There are a lot of discussions that are going on to find a compromise," Mr. Cagle said.