There is a notion behind MinMinPhx's statement that "Democrats want them to become citizens because they can buy their votes with promises of “free” healthcare, education, and welfare." and it comes from Republican endorsed policies.
Ronald Reagan openly and proudly stated that by granting 3 million illegals citizenship, he was handing the Republican Party 3 million thankful voters.
George W Bush - eager to be seen as a Reagan emulator - also stated the same in his proposed plan to grant citizenship to 10 million illegals. In addition, he suggested giving them benefits galore, including immediately becoming eligible for Social Security without having paid a cent into it like citizens are required to over many years of employment.
Then there's "Foot on the Ground" immigrants who are almost always granted citizenship simply by having come from places like the USSR, Cuba, Korea...
Republicans never stop reminding them that somehow they're the only ones responsible for the program, which also includes free rent for 18 months (used to be 24), living expenses, school, medical benefits, plus grants and interest free loans to start businesses, etc. That's why, for example, the majority of Cubans are Republicans, unlike all other Hispanics whose majorities tend to lean Democrat.
Such brazenly cynical ploys are typical of the myopic Republican mindset, and thus is what they project as the motives of others.