CEOs of major tech companies are anxious about publicly challenging President Trump over refugees and other topics. The reason: they fear Trump will single them out for outsourcing jobs or shut down the so-called H-1B visa program they use to hire high-skilled foreign employees for crucial engineering and technical jobs.

White House officials tell us they are right to be nervous, especially about changes to the visa program. Chief strategist Steve Bannon and policy chief Stephen Miller are known to be deeply skeptical of the program, and will have a strong, vocal ally when Jeff Sessions gets confirmed as Attorney General.

Trump's mixed messages: On the campaign trail, he promised to "end forever the use of H-1B as a cheap labor program." He later signaled in a meeting with tech leaders that he's most concerned about companies misusing the visas to displace lower-wage American workers.

How it works: Visas are capped at 65,000 a year, with 20,000 additional visas for foreign workers with master's degrees. The demand for the visas is so high that the cap is usually exceeded within a few days of the application window opening. The visas are distributed to companies through a lottery system.

Tech companies such as Microsoft, Google, IBM, Cisco, Apple, Intel and Facebook say the visas are crucial for specialized jobs they can't fill domestically because of a shortage of American graduates with the right technical skills. When CEOs spoke out over the weekend about the ban, they pointed out the importance of allowing the "best and brightest" to work in the U.S.

What to watch: Short of shutting down the visas, Trump could administratively strangle the program or work with Congress to significantly slash it, immigration experts told Axios.

• Ramp up enforcement: Sen. Jeff Sessions, Trump's pick for attorney general and long-time critic of H-1Bs, could ratchet up scrutiny of the application process and impose such severe penalties and fines that companies will stop using the program. The Justice Department can bring more serious charges relatively easily under existing policies.
• Raise wage requirements: Congress could pass a bill to force companies to pay H-1B visa holders higher salaries to ensure the program isn't used to replace lower-level American workers. Congress could also increase Department of Labor oversight of H-1B dependent companies, or firms with more than 15 % of workers relying on the visas. Rep. Darrell Issa, a Trump supporter, is pushing legislation that would, through government oversight, force those companies to pay all H-1B workers at least $100,000 a year, up from the current minimum of $60,000.
• Reprioritize the lottery: The current lottery system is first come, first served. The Department of Homeland Security could possibly rejigger the system so H-1B visa allocation is prioritized based on salary or even the manner in which companies use H-1B workers.
• Reduce the numbers: Cutting back the number of H-1B visas up for grabs requires legislation. DHS could also find ways to restrict access to the visas for certain types companies.
• Increase headaches: The administration could hike up the fees companies pay to apply for the visas to discourage bulk filings. Officials could simply divert resources away from the H-1B program to slow down application processing, or require so many new screenings or background checks that companies give up on the program.
• Shame into submission: Fears of being the subject of a Trump tweetstorm shaming big H-1B users could prompt companies to cut back on their visa applications. Even tech companies that follow the program's rules to the letter would prefer to avoid a PR nightmare.