The problem is that the Senate is currently in "pro forma" sessions, where they do just enough to be technically operating. This was done for another reason (blocking recess appointments) but has a bearing here.
Some have argued that the pocket veto can be used in this case. I disagree. To quote the US constitution:
Article 1, Section 7:
If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it, unless the Congress by their Adjournment prevent its Return, in which Case it shall not be a Law.
That's the pocket veto in bold. So the key phrase is "Congress must be Adjourned". What does it take to do that?
Aticle 1, Section 5:
Neither [House of Representatives or Senate], during the Session of Congress, shall, without the Consent of the other, adjourn for more than three days, nor to any other Place than that in which the two [sections] shall be sitting.
Did the Senate consent to the House of Representatives being out of session? I doubt it. Therefore the House of Representatives and the people in it are, in a phrase, AWOL, and Congress is not Adjourned, and the pocket veto cannot be used. QED.