The Act was sponsored by two Democrats; H.R. 5678 was named after its sponsors, Senator Pat McCarran (D-Nevada), and Congressman Francis Walter (D-Pennsylvania).
Speaking in the Senate on March 2, 1953, the Democrat, McCarran, said (Senator Pat McCarran, Cong. Rec., March 2, 1953, p. 1518):
I believe that this nation is the last hope of Western civilization and if this oasis of the world shall be overrun, perverted, contaminated or destroyed, then the last flickering light of humanity will be extinguished. I take no issue with those who would praise the contributions which have been made to our society by people of many races, of varied creeds and colors. ... However, we have in the United States today hard-core, indigestible blocs which have not become integrated into the American way of life, but which, on the contrary are its deadly enemies. Today, as never before, untold millions are storming our gates for admission and those gates are cracking under the strain. The solution of the problems of Europe and Asia will not come through a transplanting of those problems en masse to the United States. ... I do not intend to become prophetic, but if the enemies of this legislation succeed in riddling it to pieces, or in amending it beyond recognition, they will have contributed more to promote this nation's downfall than any other group since we achieved our independence as a nation.America is the last hope of Western Civilization and if overrun by any creed (such as Islamism) or any race (i.e., Hispanic or others) that does not assimilate or are enemies the nation will decline as a result.
In fact, Federal law does permit a president to ban those who are deemed security risks from entering the country. The relevant passage states:
"Whenever the President finds that the entry of any aliens or of any class of aliens into the United States would be detrimental to the interests of the United States, he may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate. Whenever the Attorney General finds that a commercial airline has failed to comply with regulations of the Attorney General relating to requirements of airlines for the detection of fraudulent documents used by passengers traveling to the United States (including the training of personnel in such detection), the Attorney General may suspend the entry of some or all aliens transported to the United States by such airline."
Cf. https://www.law.cornell.edu/uscode/text/8/1182