I got contacted by another recruiter yesterday morning and was told up-front that their client, some government, can only hire citizens since it needs clearance...
So today I got smart and called the recruiter before I even began to modify my resume to emphasize my skills and experience that fit the position. It turned out citizenship is not necessary even though the project is sited at government.
With GC and citizenship, we have many more opportunites here in the U.S. to make a better living (still just making a living, though, hehe)