Something I haven't seen discussed yet: McConnell's possible reasoning

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5. You are mistaken that the Senate would override a Trump veto.

The fact that the Senate voted by voice vote to approve a short term funding stopgap on December 19 without border wall funding is irrelevant.

For one thing, that bill passed when the republicans thought Trump supported it. For another thing, it was a different bill than the one(s) passed by the House. The December 19 bill funded the entire government only through February 8. The House bills fund the government through September, except for DHS, which is only funded through February 8 (which is only a month compared to the 7 weeks it would have been if passed when originally considered).

I'm not defending what McConnell is doing, but it isn't because the Senate would override. He just wants to protect Republicans from having to vote on the bill.