Embarrassing doesn’t begin to tell the story.  And we don’t make this criticism lightly.  That said, this is a move more fit for an amateur politician, than an outstanding Army veteran and rare successful member of the Republican party in New York.
WGY was the first to report on Republican 

Congressman Chris Gibson’s willingness to cave in on tax hikes to avert the fiscal cliff.Another Republican signals that he’s willing to consider tax increases in dealing with the fiscal cliff. This time, it’s Capital Region and Hudson Valley Congressman Chris Gibson. He signed the no tax hike pledge when he ran for Congress two years ago in the 20th District and won.

Mention of the district Gibson was victorious in is key here, as he is now citing redistricting and the re-numbering of that district as a reason for no longer being beholden to the pledge.

Representative Gibson now says he signed his pledge in 2010 when he was a candidate for Congress. But the pledge was made to the people of New York’s 20th congressional district. Since then, the new Census mandated a redrawing of the district lines which included changing the number of the district Gibson was in. So his office now claims: “Congressman Gibson doesn’t plan to re-sign it for the 19th Congressional District, which he now represents (the pledge is to your constituents of a numbered district).”

The absurdity of that statement is so egregious that Mr. Gibson owes an apology to the roughly 50% of district 20’s constituents that still fall under his representation for not keeping his no-tax pledge, and a separate apology to his new constituents in district 19 for insulting their intelligence.
The Review article continues:

This comical maneuver should make Representative Gibson a laughing-stock. What if the New York legislature had kept his district number the same? Would he then be bound by it? 

Trending: Rand Paul, Andy Biggs: If We Keep Listening to Fauci, There Won’t Be an America to Reopen

About half of his new constituents were also in his old 20th district. Doesn’t his pledge to them still hold? 

The technical loophole that Gibson claims to have found doesn’t even hold up. The ATR pledge, which all but six House Republicans had signed in the run-up to this November’s election is addressed “to the taxpayers of the ____ district,” with candidates expected to fill in the blank. 

But the next line says the pledge is also made “to the American people.” Grover Norquist of ATR says the pledge was worded in that way to account for the fact that district numbers would change.

It’s tempting for the Republicans to panic right now and abandon their principles.  But don’t weasel your way out of it with an intellectually dishonest excuse.  At the very least, admit that you’re willing to negotiate your principles based on election results.
For the rest of the conservative Republicans out there – it’s okay to stick to your guns.  It is okay to maintain your position on something you believe in.  Devolving morally is for the other party.  Keeping your word should still matter in ours.