Washington (CNN) Businesses and some pro-economic growth Republican think tanks are worried about President Donald Trump's immigration policies -- and they're hoping that maybe the businessman in chief might be influenced by their message.

Their appeal to the famous negotiator: Think about the economy.

In just over a week of his presidency, Trump has already issued a handful of executive orders regarding immigration, including Friday's directive banning entry to the US of nationals from seven Muslim-majority countries.

The order also prompted a swift backlash from a range of businesses. Tech companies and their executives, including Facebook, Apple, Google, Lyft, Netflix and Twitter, issued rebukes of Trump's actions and pledged to help employees and individuals affected by it. Travel companies like Expedia and Trip Advisor followed suit in expressing concern, as did a host of other businesses ranging from Ford to General Electric.

The business world is now hoping to find a way to get the White House's ear on the issue and drive home an economic appeal to a President whose business background has been his main selling point.

One lobbyist with clients in multiple sectors affected by the ban said groups are trying to figure out how to translate their concern to a new administration that has been chilly to lobbying and has limited previous ties to K Street, Washington's center of lobbying.

"There is a clear effort going on on K Street to figure out the right ways to get to the administration to explain to them the negative economic impacts of some of the things they're thinking about doing and are doing," said the lobbyist, who spoke on condition of anonymity to protect his clients.

The crafting of Trump's order has been mainly ascribed to his top adviser Steve Bannon and senior policy adviser Stephen Miller. The impetus, according to the White House and the order, has been to fight terrorism and ensure that individuals coming to the country are properly vetted.

Neither Bannon nor Miller have wide connections in Washington, making it difficult for lobbying groups to get their concerns heard on the orders.

"I think the challenge is that it appears to be a very small inner circle who are making these decisions and trying to figure out how to have real contact with that inner circle is challenging," the lobbyist said.

The White House did not respond to a request for comment. It has defended the rollout of the order, saying those who needed to be included were and that the action was taken with the urgency of security in mind.

At first after the issuance of the order, even permanent legal residents that held US green cards who were born in the seven countries affected were being detained at US airports or turned back. Others with valid visas faced the same fate. The White House has since reversed course and said green card holders are not affected by the order, unless they are flagged for posing a threat, and that others may be allowed in on a case-by-case basis.

But businesses fear that damage may already be done: Employees are unable to leave the country for fear of not being able to return, and potential tourists and clients may choose to avoid the US over concern that they not be let in -- especially given the White House leaving open the possibility of adding more countries.

And in industries like the tech and engineering sector, companies rely heavily on an international talent pool, making preserving high-skilled immigration visas a key concern for their bottom lines.

Trump has made business a key focus of his administration alongside security -- and CEOs are hoping that they can appeal to him on that side of the equation.

Several of his critics are already on Trump's manufacturing or economic committees, which he meets with periodically, and are hoping to use that to their advantage.

Tesla CEO Elon Musk and Uber CEO Travis Kalanick both took to Twitter over the weekend to say they'd bring their and other concerns to Trump directly.

"Please read immigration order. (Let me know) specific amendments. Will seek advisory council consensus & present to President," Musk tweeted with a link to the text.

"I'm going to use my position on Pres economic council to stand up for what's right," tweeted Kalanick.

Ford CEO Mark Fields told CNN's Poppy Harlow that he would stay on the council, despite having concerns about the particular policy. Asked if he would bring up the ban, he said: "We will always be straight forward. We'll do it with candor, but we'll also do it with respect."

It's not just businesses, either. A raft of conservative and center-right think tanks are making the case that pro-immigration policies are in the whole nation's economic interest.

Immigration needed to hit growth targets

At a conference on immigration reform held by the pro-market Reason Foundation on Monday, Hoover Institution fellow Tim Kane gave a presentation saying that immigration reform -- done to keep up the legal flow of immigrants into this country -- would be essential if Trump wants to meet his economic goals otherwise.

"Immigration reform will be essential to hit that 4% growth target, because without immigration, you're not going to be able to hit that 4% growth," Kane said, adding that he was optimistic the Trump administration would be on track given its decision to not rescind protections for undocumented immigrants brought here as children in its first week.

Daniel Griswold, a fellow at George Mason University's pro-market Mercatus Center, said in a later panel that the Trump administration could vastly decrease illegal immigration by making it easier to legally hire low-skilled immigrants

"Expanding legal immigration I believe is the key to fixing our entire immigration system," Griswold said, citing a CATO Institute study that found increasing low-skilled immigration would boost GDP by more than 1%.

And on Friday, another scholar at the center-right CATO Institute told a Migration Policy Institute event on the Deferred Action for Childhood Arrivals program, the protection for the so-called DREAMers who were brought here as children, said adopting a hard-line policy like deporting all of the 750,000 people in DACA would cost the US $280 billion in reduced economic growth over 10 years, according to his study

"This cost is not trivial," said Ike Brannon, a CATO visiting fellow. "This cost of repealing this is enough money that I think you would probably have to score this (were it to go before Congress), and if you score this, you're going to find you're creating a hole in the federal budget."

Though the White House has indicated deporting DACA recipients is not a priority, an order last week set enforcement priorities for deportation that could include DACA recipients, depending how immigration officers interpret it.