“To the degree that we thought it would be easier for it to happen here given the progressive leadership, that’s not true,” said Emmanuel Caicedo, the senior campaign strategist for Demos, a left-leaning public policy group that champions the credit check law along with other nonprofits. “It’s still an uphill struggle.”

Welcome to policy making in the de Blasio era. The mayor takes pride in his liberal agenda and the concrete steps he has taken to improve the lives of ordinary working people. But he has also displayed a pragmatic streak that has pleasantly surprised some business leaders while unsettling some allies on the left.

Remember his expansion of the living wage law? Mr. de Blasio originally wanted to eliminate all but three loopholes in that law, which requires companies that receive more than $1 million in city subsidies to pay workers more than minimum wage. But in the end, he offered more exemptions and covered fewer industries than planned.

The mayor’s aides said his thinking on the living wage evolved as he and his team dug more deeply into city subsidy data. And in considering the credit check law, city officials started suggesting months ago that they wanted to hear from all sides — employers and workers, advocates and council members — to try to work out a common-sense approach that might well include some exemptions.

Image City Councilman Brad Lander, a Brooklyn Democrat, helped persuade a majority of his colleagues to support a credit check bill that he said would not be “riddled with loopholes.” Credit... Karsten Moran for The New York Times

Mr. Lander pointed to a 2010 study by the Society for Human Resource Management that found that 60 percent of the firms surveyed relied on credit checks in hiring. (In New York City, credit checks are even sometimes used to screen dog walkers and janitors.) Employers say the checks are necessary at a time when identity theft and cybercrimes are rife, but advocates say they disproportionately harm blacks and Hispanics without accurately predicting fraud or poor job performance.