Pritzker set for May 23 nomination hearing

He said that detractors are just looking at the money and not at her qualifications. 

"She's extremely competent," Rockefeller said. 

Pritzker is the heiress to the Hyatt hotel fortune with a net worth of $1.85 billion, making her the 277th richest person in the United States, according to Forbes. 

She has been making the rounds on Capitol Hill this week, talking to the members of the committee about her background and what she can bring to the Commerce job. 

Sen. Mark BegichMark Peter BegichPerez creates advisory team for DNC transition The future of the Arctic 2016’s battle for the Senate: A shifting map MORE (D-Alaska), a member of the Commerce panel, met with Pritzker on Tuesday where they discussed sound fisheries management — 55 percent of America’s domestically caught seafood is harvested in Alaska — as well as Arctic development.

“When it comes to Alaska, we like to call the Secretary of Commerce the Secretary of Fish," Begich said in a statement. 

"With a majority of our country’s domestic seafood being harvested in Alaska, I hope that Penny is looking forward to brushing up on her fisheries knowledge,” he said. 

“I feel confident that if confirmed, she will make it a priority to visit Alaska in the near future and learn more about Arctic development.”

As a member and co-founder of the Senate Tourism Caucus, Begich also discussed with Pritzker the importance of expanding tourism jobs as well as the implementation of the Travel Promotion Act.

But Pritzker's nomination faces some scrutiny, too. 

Sen. Charles GrassleyCharles (Chuck) Ernest GrassleyGOP moves to cut debate time for Trump nominees Democrats fret over GOP changes to Mueller bill Let Robert Mueller do his job MORE (R-Iowa) said he is concerned about Pritzker's offshore holdings and has urged the Commerce Committee to delve more deeply into the issue. 

"It isn't just about her. It isn't about the offshore stuff. It's about the fact that the president made a big deal out of Romney having offshore [accounts], and you would think that if that's a big deal for who you're running against for president, that the president of the United States wouldn't be appointing people who make use of that in his own Cabinet," Grassley told The Hill. 

"In other words, if it's wrong, it's wrong."

He said it is possible that she could lose his vote if there are major financial questions. 

"Yeah, it's possible. I'm going to wait until I read what the Commerce Committee does."

Jordy Yager contributed.