Barro notes that increasing unemployment insurance lowers the probability a job seeker will accept a new job, and the economy is always creating and destroying a lot of jobs:
For example, the Bureau of Labor Statistics reports that, near the worst of the recession in March 2009, 3.9 million people were hired and 4.7 million were separated from jobs. This net loss of 800,000 jobs in one month indicates a very weak economy—but nevertheless one in which 3.9 million people were hired. A program that reduced incentives for people to search for and accept jobs could surely matter a lot here.
But, for the other side, the issue is rather simple. If we did not give people unemployment insurance, they would die. Here's American Prospect columnist Tim Fernholz explaining his utter disdain for Jim Bunning, the congressman who tried to block increasing unemployment insurance without funding it first.