Here is the House publication detailing the GOP's stance on immigration. It starts with a secure border and builds on that.

Editor's notes:  When thoughtful conservatives read this statement,  it is  hoped they will see little with which to be concerned,  from a conservative point of view.  The highlighted (in read) comments should set the conservative mind at ease.    (the highlights are mine - blog editor).  With all this talk about "amnesty,"  read the highlighted comments over and over,  and remember that border security remains critically important to House Leadership.  What is being called "amnesty" by members of my side of the aisle,  is actually "legal status" for those who have admitted their illegal presence in this country, and have complied with specific remedies.  For Leadership,  the "path to citizenship" includes the demand that these folks go to the back of the line,  and wait their turn for citizenship.  While they wait,  they have legal status.  This is not an "amnesty" that is equivalent to "citizenship."   But that is,  often,  how this term is used by those who believe these illegals,  and they are here illegally,  must be rounded up in mass,  and sent back to Mexico.   

Update to the above:  I must add this: what I do not understand about this debate, has to do with why politicians on both sides of the equation do not talk about the fact that we already have an immigration system.  All of the House Principles detailed below,  are compatible with stream-lining the current system,  solving the border security problem and using using the new and improved,  streamlined immigration system,  as the answer to all of this noise about "comprehensive immigration."  

Standards for Immigration Reform

Preamble

Our nation’s immigration system is broken and our laws are not being enforced. Washington’s failure to fix them is hurting our economy and jeopardizing our national security. The overriding purpose of our immigration system is to promote and further America’s national interests and that is not the case today. The serious problems in our immigration system must be solved, and we are committed to working in a bipartisan manner to solve them. But they cannot be solved with a single, massive piece of legislation that few have read and even fewer understand, and therefore, we will not go to a conference with the Senate’s immigration bill. The problems in our immigration system must be solved through a step-by-step, common-sense approach that starts with securing our country’s borders, enforcing our laws, and implementing robust enforcement measures. These are the principals guiding us in that effort.

Border Security and Interior Enforcement Must Come First

It is the fundamental duty of any government to secure its borders, and the United States is failing in this mission. We must secure our borders now and verify that they are secure. In addition, we must ensure now that when immigration reform is enacted, there will be a zero tolerance policy for those who cross the border illegally or overstay their visas in the future. Faced with a consistent pattern of administrations of both parties only selectively enforcing our nation’s immigration laws, we must enact reform that ensures that a President cannot unilaterally stop immigration enforcement.

Implement Entry-Exit Visa Tracking System

A fully functioning Entry-Exit system has been mandated by eight separate statutes over the last 17 years. At least three of these laws call for this system to be biometric, using technology to verify identity and prevent fraud. We must implement this system so we can identify and track down visitors who abuse our laws.

Employment Verification and Workplace Enforcement

In the 21st century it is unacceptable that the majority of employees have their work eligibility verified through a paper based system wrought with fraud. It is past time for this country to fully implement a workable electronic employment verification system.

Reforms to the Legal Immigration System

For far too long, the United States has emphasized extended family members and pure luck over employment-based immigration. This is inconsistent with nearly every other developed country. Every year thousands of foreign nationals pursue degrees at America’s colleges and universities, particularly in high skilled fields. Many of them want to use their expertise in U.S. industries that will spur economic growth and create jobs for Americans. When visas aren’t available, we end up exporting this labor and ingenuity to other countries. Visa and green card allocations need to reflect the needs of employers and the desire for these exceptional individuals to help grow our economy.

The goal of any temporary worker program should be to address the economic needs of the country and to strengthen our national security by allowing for realistic, enforceable, usable, legal paths for entry into the United States. Of particular concern are the needs of the agricultural industry, among others. It is imperative that these temporary workers are able to meet the economic needs of the country and do not displace or disadvantage American workers.

Youth

One of the great founding principles of our country was that children would not be punished for the mistakes of their parents. It is time to provide an opportunity for legal residence and citizenship for those who were brought to this country as children through no fault of their own, those who know no other place as home. For those who meet certain eligibility standards, and serve honorably in our military or attain a college degree, we will do just that.

Individuals Living Outside the Rule of Law

Our national and economic security depend on requiring people who are living and working here illegally to come forward and get right with the law. There will be no special path to citizenship for individuals who broke our nation’s immigration laws – that would be unfair to those immigrants who have played by the rules and harmful to promoting the rule of law. Rather, these persons could live legally and without fear in the U.S., but only if they were willing to admit their culpability, pass rigorous background checks, pay significant fines and back taxes, develop proficiency in English and American civics, and be able to support themselves and their families (without access to public benefits). Criminal aliens, gang members, and sex offenders and those who do not meet the above requirements will not be eligible for this program. Finally, none of this can happen before specific enforcement triggers have been implemented to fulfill our promise to the American people that from here on, our immigration laws will indeed be enforced.