When you refrain from raising someone's taxes, you are not "giving" them anything. Even if you were actually cutting their tax rate-- which is out of the question today-- you would still not be "giving" them anything, but only allowing them to keep more of what they have earned.
Is the government doing any of us a big favor by not taking even more of what we have worked for? Is it not an insult to our intelligence to say that the government is "giving" us something by not taxing it away?
With unemployment compensation, however, you are in fact giving someone something. "Extending unemployment benefits" always sounds good politically-- especially if you do not ask the basic question: "For how long should they be extended?" A year? Two years? No limit?
Studies have shown what common sense should have told us without studies: The longer the unemployment benefits are available, the longer people stay unemployed.
If I were fired tomorrow, should I be able to live off the government until such time as I find another job that is exactly the same, making the same or higher pay? What if I am offered another job that uses some of the same skills but doesn't pay quite as much? Should I be allowed to keep on living off the government?
With the government making it more expensive for employers to hire workers, and at the same time subsidizing unemployed workers longer and longer, you can have as much unemployment as you are willing to pay for, for as long as you are willing to pay for it.