They say Manpower, for example, last year posted US job openings in India but not in the United States.
"We have a shortage in the industry all right - a shortage of fair and ethical recruiting and hiring," said Donna Conroy, director of Bright Future Jobs, a group of tech professionals fighting to end what it calls "discriminatory hiring that is blocking us ... from competing for jobs we are qualified to do."
"US workers should have the freedom to compete first for job openings," Conroy said.
Infosys spokesman Paul de Lara responded that the firm encourages "diversity recruitment," while spokesman Doug Shelton said IBM considers all qualified candidates "without regard to citizenship and immigration status." Manpower issued a statement saying it "adopts the highest ethical standards and complies with all applicable laws and regulations when hiring individuals."
Much of the backlash against the H-1B and other visa programs can be traced to whistleblower Jay Palmer, a former Infosys employee. In 2011, Palmer supplied federal investigators with information that helped lead to Infosys paying a record $34 million settlement last year. Prosecutors had accused the company of circumventing the law by bringing in lower-paid workers on short-term executive business visas instead of using H-1B visas.
Last year, IBM paid $44,000 to the US Justice Department to settle allegations its job postings expressed a preference for foreign workers. And a September trial is set against executives at the staffing company Dibon Solutions, accused of illegally bringing in foreign workers on H-1B visas without having jobs for them - a practice known as "benching."
In court papers, Parker claims that she was given positive reviews by supervisors, including at Infosys, which she maintains oversaw her work and the decision to let her go. The only complaint: Her desk was messy and she'd once been late.
Neither Parker nor other workers involved in similar lawsuits and contacted by The Associated Press would discuss their cases.
Parker's attorney, Dan Kotchen, noted that the case centers on discrimination based on national origin but said that "hiring visa workers is part of how they obtain their discriminatory objectives."
Infosys is seeking a dismissal, in part on grounds that it never hired or fired Parker. Parker was hired by a different subcontractor and kept on, initially, after Infosys began working with Harley-Davidson.
A company spokeswoman said Infosys has about 17,000 employees in the US, about 25 per cent US hires. In filings to the US Securities and Exchange Commission, the company said it has more than 22,000 employees with valid temporary work visas, some not in the US.
Stanford University Law School fellow Vivek Wadwha, a startup adviser, said firms are so starved for talent they are buying up other companies to obtain skilled employees. If there's a bias against Americans, he said, it's an age bias based on the fact that older workers may not have the latest skills. More than 70 per cent of H-1B petitions approved in 2012 were for workers between the ages of 25 and 34.
"If workers don't constantly retrain themselves, their skills become obsolete," he said.
Norm Matloff, a computer science professor at the University of California, Davis, agreed that age plays into it - not because older workers are less skilled but because they typically require higher pay. Temporary workers also tend to be cheaper because they don't require long-term health care for dependents and aren't around long enough to get significant raises, he said.
Because they can be deported if they lose their jobs, these employees are often loath to complain about working conditions. And even half the standard systems analyst salary in the US is above what an H-1B holder would earn back home.
Such circumstances concern Americans searching for work in a still recovering economy.
Jennifer Wedel of Fort Worth, Texas, publicly challenged Obama on the visa issue in 2012, making headlines when she asked him via a public online chat about the number of foreign workers being hired - given that her husband, a semiconductor engineer, couldn't find work.
Wedel said her husband eventually found a job in the health care industry, taking a $40,000 pay cut.
"It's a slap in the face to every American who worked hard to get their experience and degrees and has 10 or 15 years of experience," she said, adding that firms want that experience but don't want to pay for it.
To her, the issue isn't about a shortage of workers who have the right skills. Put simply, she said: "It's the money."