The state legislature strongly approved the measure in the closing hours of the session in June, but the bill has sat on the governor's desk for more than five months as he weighs the proposal.
The cap would mean a property valued at $100,000 last year could be taxed only up to $120,000 this year, regardless of how high the market value climbed.
Supporters expect to have the two-thirds approval needed for an override if the cap is vetoed, but several legislators said concerns about education funding and constitutional questions will have to be addressed.
The governor said last month he was concerned by a voice vote to approve the proposal in the Senate, constitutional requirements to tax property at the fair market value and recent studies critical of the plan.
Sen. Scott Richardson, R-Hilton Head Island, said Wednesday that he would not be surprised by a veto.
"(Sanford has) had problems with it all along," he said.
Freshman Rep. Richard Chalk, R-Hilton Head Island, said legislators will have to carefully consider overriding any veto.
"It was done quickly, and there are some constitutional questions," he said. "I'm sure there are alternative ways to remedy the problem."
The state's use of property values to distribute tax dollars to schools is a concern for several legislators.
An October study by the S.C. Chamber of Commerce states that limiting the property values in a county will have an impact on the distribution to school districts.
"The most important factor will be information as it relates to school funding," Richardson said.
Although Beaufort and Charleston counties should see an increase in school funding, according to the chamber report, most other counties would lose money if property isn't assessed at its full market value.
But leaving the property tax system as it is will not be an option, Richardson said.
"The public is screaming for property tax relief," he said. "My calls are 100 to one to support this thing."
Although against the cap, Rep. Thayer Rivers, D-Ridgeland, said he understands property taxes are affecting homeowners.
"It's not just uncomfortable, it's crippling," he said.
The House had approved the cap, 104-5, suggesting strong support for an override, if necessary, said Rep. Catherine Ceips, R-Beaufort, who voted for the cap.
"Considering the overwhelming support of the bill," she said, "it'll be brought up."
But the Senate's voice vote in June has some, including the governor, questioning the bill's legitimacy.
"For something this important, you should stand on your record," said Sen. Clementa Pinckney, D-Ridgeland, who voted against the cap.
Pinckney said the tax cap was bad policy and a would cause a shift in the tax burden from wealthy property owners to those not as well off.
Another chamber study released in October stated that while some Beaufort County residents would see a tax cut, 73 percent of Beaufort taxpayers would pay more taxes if the cap were imposed.
"No one has been able to justify why someone in Sheldon or on St. Helena should pay for a beach house on Hilton Head," Pinckney said.
On a local level, Beaufort County's local governments are expected to have a $40 million hole in revenues if the cap is approved, according to Tom Henrikson, Beaufort County controller.
A cap would require refunds and rebilling for property owners who overpaid on their tax bills, but the governments couldn't rebill other taxpayer to recoup those lost dollars.
That would leave the county, school district, municipalities and various public service districts with no option but to borrow the money to meet budget needs and add those costs to tax bills next year.
Rep. Bill Herbkersman, R-Bluffton, said the state may see an exodus without some form of property tax relief.
"We need to look at the long-term costs," he said.
State Rep. Walter Lloyd, D-Walterboro, couldn't be reached for comment.