"The president wants to be able to play both sides of this issue. He's obviously concerned about what's going on in North Carolina. He doesn't want to fully embrace what his vice president is saying, but he wants the benefit of what the vice president is saying," said Priebus on MSNBC's "Andrea Mitchell Reports."
Biden said he supports same-sex couples having "the same exact rights" as heterosexual couples.
"I am Vice President of the United States of America," Biden said on NBC’s "Meet the Press." "The president sets the policy. I am absolutely comfortable with the fact that men marrying men, women marrying women and heterosexual men marrying women are entitled to the same exact rights."
On Monday, Secretary of Education Arne Duncan was asked if he believed same-sex couples should be allowed to wed legally. "Yes, I do," Duncan said on MSNBC's "Morning Joe."
Asked if he had acknowledged that publicly before, Duncan said, "I don't think I've ever been asked publicly."
Obama, however, has not endorsed same-sex marriage and has described his views on the matter as “evolving.”
The president has publicly opposed a proposed amendment to North Carolina’s state constitution, which would define marriage as a union between a man and a woman, as “divisive and discriminatory.”
North Carolina voters will vote on the amendment during a referendum Tuesday, May 8.
Democratic and Republican leaders, including former President Clinton and former House Speaker and one-time GOP presidential hopeful Newt Gingrich, have come out on opposite sides of the state amendment, lending it greater national recognition and scrutiny.
The upcoming referendum and Biden’s comments have again focused attention on Obama’s stance on the issue, which has angered pro-gay-rights groups that want him to wholeheartedly support same-sex marriage.
Priebus told MSNBC uncertainty over the administration’s stance on gay marriage highlighted Obama's greatest vulnerability in the upcoming election, that voters would view him as "not authentic anymore."
"People just aren't buying what he's selling, because they don't believe it's real anymore — that it's politics. He has become the ultimate Washington politician and this latest episode in regard to gay marriage is a great example of that," Priebus said.
When asked to state the Republican stance on gay marriage, Priebus said, "I think Gov. Romney and the Republican Party have been pretty clear. We believe marriage is between one man and one woman."
"We believe ultimately that you can't federalize that kind of mandate, which is why we believe individual states can make those decisions on their own and their doing that across the country. So we've been clear," he added.
Asked by reporters to clarify the president’s stance on the issue, senior campaign strategist David Axelrod on Monday pivoted to presumptive GOP nominee Mitt Romney’s views on gay marriage.
“There couldn't be a starker contrast on this issue than with Gov. Romney, who has funded efforts to roll back marriage laws in California and other places," Axelrod told reporters on the call.
Priebus fought back against that assertion, saying the president's public position "as it sits today" is the same as Romney's.
"Isn't the president saying that he believes a marriage is between a man and a woman? … the difference is that Mitt Romney is being honest about his position the whole way through," Priebus said.