The McCarran-Walter bill passed both houses of Congress in 1952, but was vetoed by President Harry S Truman. Truman found many of the provisions of the bill to be needlessly restrictive and called for a more open immigration policy. As an alternative, Senators Herbert Lehman (New York) and Hubert Humphrey (Minnesota) introduced a new bill that would have allowed for the entry of tens of thousands more immigrants per year than the McCarran-Walter bill. It would have also allowed greater diversity in immigration by basing quotas on the 1950 census and by allowing the pooling of unused quotas. If a country with high quotas, such as Great Britain, did not have a sufficient number of immigrants to meet the quota, the slots intended for British immigrants could be redistributed to immigrants from countries whose yearly allotment had already been filled. While the Lehman-Humphrey bill also contained provisions to deny immigration based on political affiliations, it made deportation more difficult by ensuring a more rigorous process for proving the danger an individual poses to the United States.
Below is one letter illustrating Murray's support for the Truman veto and one letter from Senator Lehman thanking Murray for his support of the Lehman-Humphrey bill. Also note that Murray's letterhead indicates that he is the chairman of the Senate Committee on Labor and Public Welfare, a committee on which both Humphrey and Lehman served.