Sanford said the bill, which would have imposed a 20 percent cap on increases in property values on homes and businesses, is unconstitutional because it doesn't tax property based on fair market value.
The bill was intended to help people who have seen their properties skyrocket in value avoid drastically higher property taxes.
The state constitution requires that homes be assessed at fair market value, Sanford said Friday, and a reassessment cap does not fulfill that requirement.
"I'm more than open to considering any property tax relief proposal that passes constitutional muster," he said.
Local legislators conceded Friday that some legal issues do surround the proposed cap but vowed to push for the override in the early days of the next legislative session, which starts Jan. 11.
Property reassessments, typically completed every five years, are already lagging behind fair market value, said state Sen. Scott Richardson, R-Hilton Head Island, who added the cap amendment to an unrelated bill in the closing days of last year's legislative session.
"I think it's a shallow argument," he said of the governor's veto.
But Richardson shared Sanford's concerns over how property assessments are used to determine the amount of money the state funnels to school districts.
Under the cap, the wealth of counties like Beaufort would be underrepresented, taking state dollars away from poorer school districts, the governor said.
"In this instance it would result in a significant shift in education funding that I don't believe has been fully considered," Sanford said.
Concerns surrounding a shift in school funding were listed in a South Carolina Chamber of Commerce study released in October and were reaffirmed by an analysis completed by the state departments of revenue and education.
Although the cap was talked about for several months in Columbia, Richardson said the impact on education wasn't discussed before the legislature voted.
"That's one of the things we're going to have to look at," he said.
Rep. Catherine Ceips, R-Beaufort, said Friday she's already been fielding calls from several legislators preparing to override the veto, which requires a two-thirds vote from members of the House and Senate.
Richardson said he expects to have the votes necessary for an override but is prepared to offer up an alternative if necessary.
"I think the will is there for some form of property tax relief," he said.
In a letter to the legislature regarding the veto, the governor noted that he's willing to consider point-of-sale reassessments, or reassessing properties when they are sold.
"Simply assessing property at the time of sale would protect the property owner with long-held family property while at the same time staying true to the fair market value clause of the state constitution," Sanford's letter states.
Beaufort County Council Vice Chairman W.R. "Skeet" Von Harten, who has opposed the cap, said Friday that he agreed with the governor's findings.
"It shifts the burden on those lesser valued properties, and that's just not fair," he said.
Another study completed by the state chamber found that 73 percent of Beaufort County taxpayers would see their tax bills go up under a cap.
"There's more than one way to skin a cat," Von Harten said, adding that he'd consider alternative tax relief plans.
Beaufort Mayor Bill Rauch said the veto allows local governments to stave off budget problems expected from a cap.
"It's not as dire as it was yesterday," he said.
If the veto is overridden, all of the county's taxing entities would have to recalculate this year's tax bills and offer up refunds to people who paid too much while not being able to raise taxes on those who underpaid.
The expectation, according to county Controller Tom Henrikson, is that the county, municipalities, school district and various public service districts would have to borrow millions to fill what could become a $40 million budget hole created by a cap.
Rep. Bill Herbkersman, R-Bluffton, said he supports an override of the veto and feels tax relief must come immediately.
House Minority Leader Harry Ott, D-St. Matthews, said he supported the legislation when it came through the House, but after further review, "This is one of those instances where I believe I support the governor."
Ott says it appears the bill puts an unfair tax shift onto lower income properties, which was not the intention. He says he supports alternatives such as increasing sales taxes and reducing property taxes, with education funding coming from sales taxes as opposed to property taxes.
House Speaker David Wilkins, R-Greenville, said Sanford's veto sends lawmakers back to square one on their efforts to cut property taxes.
"I understand his reasoning, but this is still the most egregious tax the citizens in South Carolina face," said Wilkins.