One of the cards features a picture of the president and reads, "If this was a successful year for you, there's a 5% tax on this card."
Priebus said the card was critical of President Obama's proposal to raise taxes on wealthy Americans.
"According to Barack Obama, if you do well in America, you should always pay more and more and more and it's never enough for this president," said Priebus, discussing the card.
The RNC chairman recommended to Fox News that the Obama card should be sent to "all of your friends doing a little bit better than you."
Obama's budget, delivered to Congress on Monday, proposes ending the Bush-era tax cuts for workers making at least $250,000 a year and trimming some corporate tax breaks.
The political cards can be found on the RNC's website. The committee encourages users to send them electronically to "friends and family."
The Valentine's Day messages don't exclusively attack the president. They also slam Democratic governors, members of Congress and other administration officials, including jabs at House Minority Leader Nancy Pelosi (D-Calif.), Gov. Bev Perdue (D-N.C.) and Treasury Secretary Timothy Geithner.
One card takes aim at Vice President Joe Biden for his tendency to make verbal gaffes. "This valentine has not been approved by anyone at the White House," it reads.
"Joe Biden, if anything, has been great for our YouTube videos," Priebus said. "Whether it be all of his gaffes or his cursing that he likes to throw out there off the air or accents that he likes to use that are inappropriate, we figured we had to have a Joe Biden card."
For more on the RNC's Valentine's Day cards on The Hill's Ballot Box, click here.