Smith is due $10.15 million for 2013, while Vilma is owed $6 million in the final year of his deal.
If the players are unwilling to restructure, they could be cap casualties.
As of Friday, the Saints were about $13.5 million over the salary cap, but that was before linebacker Curtis Lofton restructured his contract. The Saints must be below the cap by March 12.
Lofton's cap figure was scheduled to be $7.1 million. But the Saints were able to drop that number to $3.1 million by replacing a scheduled $5 million roster bonus with a $5 million signing bonus that will be pro-rated over the remainder of the contract.
Information from ESPN.com's Pat Yasinskas was used in this report.