When Zina Haughton, 42, got a restraining order against her husband, Radcliffe, last October — she told a court that his threats “terrorize my every waking moment” — he became ineligible to buy a gun under federal law. But he found a way around that: he bought a gun from a private seller he found on the Internet who, unlike federally licensed dealers, was not legally required to check his background.

That is how Mr. Haughton was able to buy a handgun for $500 in the parking lot of a McDonalds that he took with him on Oct. 21 to the spa in a suburb of Milwaukee where his wife worked. There, Mr. Haughton opened fire at the spa’s pedicure station, law enforcement officials said, and kept shooting until he had killed his wife and two women she worked with and injured four other women. He then killed himself.

Cases like the Wisconsin spa shooting are at the heart of the debate raging in Washington over whether to expand background checks for all gun purchases — a proposal the Senate plans to take up on Thursday. Ms. Haughton’s brother, Elvin Daniel, a hunter who belongs to the National Rifle Association, has traveled to Washington to call for expanded background checks. “I feel that had there been a background check, had that been in place, my sister would still be with us today,” he said Wednesday.