UPDATE: 10:35 a.m. EDT — Republican National Committee Chairman Reince Priebus Sunday hinted a rule requiring a candidate to have won eight primaries or caucuses to gain a spot on the convention ballot could be dropped.

Priebus on NBC’s “Meet the Press” said the eight-state rule was adopted for the 2012 convention where Mitt Romney was selected as the GOP presidential candidate. “Why would they want Romney rules on delegates to apply?” Priebus asked.

Dropping the rule would open the way for Ohio Gov. John Kasich, who has won only one state so far, to gain traction on the convention floor. Recent polls have indicated Kasich is the only Republican candidate who consistently could beat Democrats Hillary Clinton or Bernie Sanders in the general election.

Original Story:

Republican National Committee Chairman Reince Priebus Sunday rejected the notion an open convention this summer could lead to the selection of House Speaker Paul Ryan as the GOP standard bearer and floated the possibility Vice President Joe Biden could emerge as a consensus candidate at an open convention on the Democratic side.

Priebus, in an appearance on CNN’s “State of the Union,” acknowledged the candidacy of real estate mogul Donald Trump has been problematic for the party, which had been trying to redefine itself to be more welcoming to Hispanics, blacks and other groups that traditionally have shunned it.

“People are afraid in this country,” Priebus said, sidestepping a question about whether Trump’s prediction in a Washington Post interview of a coming “massive recession” is in the offing. “They are angry with a president who hasn’t delivered. … Things have not improved. … The truth is people are concerned about the future.”

Priebus said Americans also are concerned about the security of the U.S. border and that during the general election campaign, he will work with candidates to change the tenor of the discussion to make sure “we are putting our best foot forward.” Trump has pledged to build a massive wall along the border with Mexico to stem illegal immigration, a proposal that has been reviled by Hispanics in the U.S. as well as Mexican officials.

On who will capture the nomination, Priebus predicted the Republican nominee will be “someone who’s running.” He said Ryan has no interest in winning the party nod this year, even if the convention goes to a fourth or fifth ballot.

“He doesn’t seek these things out,” and “his ego is not even there. He’s not selfish. He doesn’t think like that,” Priebus said.

But he said he could see Biden capturing the Democratic nomination should former Secretary of State Hillary Clinton face prosecution for her handling of email while she was at the State Department.

The Democrats are on the “edge of fiasco at their convention,” he said.