Possibly your best first try would be search.usa.gov to look for state as well as federal reports and websites. But their plain Bing search, like Google, does not allow very precise searching. The search for both exact phrases: "undocumented immigrants" "diabetes statistics" is TOO restrictive, and gets only 2 hits; "undocumented immigrants" diabetes statistics gets 6330. That DOES, however, drop to about 153 as you scroll down to see more hits - not an impossible number to look at. Compare Google's search for: "undocumented immigrants" diabetes statistics site:gov ("about 2300 results"), which turns out to be 435 "unique" hits on 44 pages. No doubt it's best to first look at the 8 hits for: "undocumented immigrants" "diabetes statistics" site:gov or the "18" (really 13) for: "undocumented immigrants" "diabetes statistics" site:edu - though you might well be missing some good pages that don't have those exact phrases.
Google Scholar can quickly get frustrating unless you are going through a large university's proxy login - to get access to its large number of commercial journal articles. It gets 10 hits for: "undocumented immigrants" "diabetes statistics", and a few seem to be free online. But its "about 1040" results for: "undocumented immigrants" diabetes statistics may well be that many, and they look like primarily commercial journal articles.
You can try Pubmed.gov, with fairly general searches such as: undocumented immigrants diabetes (8 articles), or immigrants diabetes statistics (144 articles, 21 of them free online). But to see the many commercial journal articles full text, you would need to be onsite at a large public university library - preferably one with a large public health or medical school. Most public universities will also provide onsite guest access to other large full text databases such as Academic Search Premier, ScienceDirect, and JSTOR.
Academic Search Premier is very reliable with "truncation" to get many word combinations: immigrant* and diabet* and statistic* gets 105 results, all of them in "scholarly/peer reviewed" journals (you can click that limiter before OR after you do a search). Adding the word "undocumented" - undocumented and immigrant* and diabet* and statistic* gets no results, except for Ebsco's "smart search" result of 17 hits, which do not look too relevant to me. Ebsco's default search is author, title, abstract, journal title, and subjects. If you "Select a field" TX-All text, it's important to use proximity search, to find where the words are fairly close together and hopefully related. TX undocumented n50 immigrant* n50 diabet* n50 statistic* confirms that those words are not near each other - even in full text. It might be worth checking the 10 articles (8 in peer reviewed) for the more general TX search: undocumented n5 immigrant* n50 diabet*.
ScienceDirect is all Elsevier journals, and a major source of full text scholarly research. It defaults to full text search, but the proximity is different: undocumented w/50 immigrant* w/50 diabet* gets 21 articles; even the more precise: "undocumented immigrant*" w/50 diabet* gets 11 articles. JSTOR is also a full text default search, and has yet another proximity format: "undocumented immigrants diabetes"~50 gets 2 articles. But "undocumented immigrants diabetic"~50 gets zero, and also "undocumented immigrants diabet*"~50 gets zero - truncation is NOT reliable in JSTOR.
Most large universities have access to Dissertations & Theses Full Text (Proquest), which defaults to full text search, and uses the same format as ScienceDirect: undocumented w/5 immigrants w/50 diabetes finds 16 dissertations or theses. As in ScienceDirect, truncation also seems to be reliable: undocumented w/5 immigrant* w/50 diabet* gets 17 dissertations. Some libraries will have other full text journal "packages", such as Springer's Springerlink and Wiley's Online Library. These last 2 are less sophisticated search engines. Springerlink gets 97 hits for: "undocumented immigrants" and diabet*; Wiley gets 111. You may be able to search many of these without logging in or going onsite - you just won't be able to see full text without buying articles at a very high price. For example, the "free" online search of ScienceDirect gets those 11 articles for: "undocumented immigrant*" w/50 diabet*, but if you are not at a subscribing library and want to see PDF online, they charge $31.50 or more per article.
