In order to apply for citizenship, dreamers would have to have been living in the US for five years as a green card holder (i.e. legal permanent resident). In order to apply for a green card, you have to either be invited by an employer, be a refugee or asylum seeker or have a close family member who is either a citizen or green card holder sponsor you. You can also marry a US citizen and have them sponsor you, but that is subject to a lot of scrutiny and can be difficult to get past INS.
The real problem is that INS limits legal immigration from Mexico to @26,000 a year and there are about 1.3 million people on a waiting list for a green card. That means the typical wait time to get a green card is about a decade and can be as long as 25 years. INS will also not allow more than 7% of legal immigration to come from any one country each year. The idea is to keep any one immigrant group from dominating immigration. This is really the fundamental flaw in the immigration system. The result of this rule is that people from far flung countries or European countries with little immigration to the US can get green cards very quickly while the line for countries with high immigration demand like Mexico is impossibly long. So, Mexicans see that it is essentially futile to try to emigrate legally and cross over illegally to be reunited with family that is already here (this is the number one reason for illegal immigration). The only way to meaningfully end illegal immigration is to open the flood gates on immigration from south of the border to reduce the line so that people applying to come to the US from south of the border can get to the US in a reasonable amount of time.