What did exist was some degree of control over borders by excluding either particular racial groups (e.g. the Chinese Exclusion Acts) or particular persons based upon personal characteristics (like incurable diseases) or actions (i.e., criminal records).  But, the overwhelming presumption was in favor of allowing immigrants to come in.

Truth be told, I think the whole emphasis on "illegal immigration" is a Republican wedge issue, predicated upon holding up those filthy darker people with strange habits, furrin languages and funny accents even when they speak English.  For the Rethugs, it works because it drives the stupid/uneducated working class whites to embrace the Republican policies so inimical to those working-class whites' own self-interest.  It's really a replay of the strategy which made Jim Crow so successful.  In Jim Crow, working class whites were given all sorts of scare stories about blacks (all of which revolved around either "the black will take your job" or "the black will take your daughter") which were to be mollified by the working class' embracing the planters' descendents and realizing that, no, they really didn't need unions and leglislation to protect them against economic exploitation because they wouldn't have to worry about the blacks.

In the 80s, I remember National Review writing about this a lot, couching it in terms of "history lessons" when, in reality, it was more like "here's the blueprint, boys."

A lot of this is behind Bushie's "guest worker" and "raise the fees for legal immigrants" programs.  Bushie pushes the guest worker program by saying "It's needed because there are a lot of jobs which Americans can't be found to do".  Accurate, but only in part.  If he were honest (he isn't, but we all know that), he would have to complete the sentence by saying "... at the wages employers are willing to pay."  

By way of example, I've read that in 1983, meat-packing plant employees in the Midwest were averaging about $11/hour with benefits.  A lot of them were unionized.  Today, those same jobs pay about $9/hour, without benefits and without union protection.  And the lines have speeded up.  That may only seem like $2/hour, but if you think that you are overlooking the effect of inflation, which makes that $11 in 1983 worth $22 today.  At the rates which the lines move today, that $22 would probably have to be more like $30 or even $35.  No American can live as a productive member of society, let alone raise a family on $9/hour.  But immigrants, particularly ones who aren't exactly legally here or won't be here beyond their guest worker visas, are just the wage slaves Bushie's campaign contributors need.

A lot of this anti-immigrant effort also goes at further undercutting unions.  Real simple:  Unions set the base level of pay, benefits and employment conditions below which employers can't go.  Removing unions removes the floor, and the race to the bottom in pay, conditions, and so on, continues.  And Rethugs love that.

Actually the NAs could have ran off the New Arrivals pretty easy. Hundreds of thousands can overome hundreds, even if the hundreds have better weapons.
The problem was morale.

Then they didn't try to take over the world and they tried to make sure every American got health care.

In any country, a certain number of people are going to be wonderful, and a certain number are going to be bad. The existence of homegrown bad guys is not an excuse to import more bad guys. In fact, we should take steps to reduce the numbers of bad people in the U.S., and one perfectly feasible way to do that is to prevent terrorists from infiltrating the U.S., whether over the borders or via visas.