Romney's website doesn't mention illegal immigration, but he has recently said that he would veto the DREAM Act if it was passed by congress: http://politicalticker.blogs.cnn.com/2012/01/04/romney-defends-dream-act-stance/
The following information on skilled immigration is taken from his plan for jobs and economic growth: http://mittromney.com/blogs/mitts-view/2011/09/believe-america-mitt-romneys-plan-jobs-and-economic-growth
ATTRACTING THE BEST AND THE BRIGHTEST
To ensure that America continues to lead the world in innovation and economic dynamism, a Romney administration would press for an immigration policy designed to maximize America’s economic potential. The United States needs to attract and retain job creators from wherever they come.
Foreign-born residents with advanced degrees start companies, create jobs, and drive innovation at an especially high rate. While lawful immigrants comprise about 8 percent of the population, immigrants start 16 percent of our top-performing, high-technology companies, hold the position of CEO or lead engineer in 25 percent of high-tech firms, and produce over 25 percent of all patent applications filed from the United States. The presence of hardworking, highly skilled immigrants in our free-enterprise system fosters a special dynamic that is recognized around the world. The net result of their successes is the creation of jobs here in America that would otherwise have been created elsewhere or, more likely, never created at all.
It makes little sense for the United States to turn away highly educated immigrants who seek to come here. It makes equally little sense to train talented foreign students in our universities but then fail to integrate them into our economy. Nearly 300,000 foreign students are enrolled in advanced degrees programs here, but the great majority will return home. We are casting away the fruits of our own investment. As has long been our American tradition, we should encourage the world’s innovators, inventors, and pioneers to immigrate to the United States and we should encourage those we train to settle and create jobs here.Raise Visa Caps for Highly Skilled Workers
As president, a first step that Mitt Romney will take along these lines is to raise the ceiling on the number of visas issued to holders of advanced degrees in math, science, and engineering who have job offers in those fields from U.S. companies. These workers would not displace unemployed Americans. Rather, they would fill high-skill job openings for which there is currently an acute shortage of labor. Even in this tough unemployment climate, as of this past spring nearly 1.25 million high-skill jobs remained unfilled.
A skills gap of that magnitude suppresses the productivity of our businesses and slows the overall economy. Highly educated immigrants would help fill that gap and get our economy rolling again. Welcoming a wider pool of highly educated immigrants would lead to more start-ups, more innovation, and more jobs. Each of these workers would in turn be consumers in local economies, creating new demand for other American products and services. Thus, for every foreign worker employed in this way, new job opportunities also arise for those who are currently unemployed.
Retain Graduates of Our UniversitiesAs president, Mitt Romney will also work to establish a policy that staples a green card to the diploma of every eligible student visa holder who graduates from one of our universities with an advanced degree in math, science, or engineering. These graduates are highly skilled, motivated, English-speaking, and integrated into their American communities. Permanent residency would offer them the certainty required to start businesses and drive American innovation. As with the highly skilled visa holders, these new Americans would generate economic ripples that redounded to the benefit of all.