In many states the court makes you pledge to judge only the facts of a case, or otherwise orients you to leave the law to the judge. This gives them the ability to prosecute you for perjury if you then do otherwise at trial. At the last jury duty pool I was part of I strenuously objected, and cited past law cases to back up jury nullification. The attorneys on BOTH sides tried to talk me out of it, finally suggesting that if I judged the law, they wouldn't know what criteria I used to reach a verdict. I was then excused from jury duty.
Such a pledge is unenforceable, because nobody is privy to what goes on in the jury room except for jurors, and as far as I know, jurors have
long been protected by law from any retalitation for their verdict. Along with privacy/discretion, the jury's protection from retaliation simply goes hand-in-hand with a real jury trial...and I haven't heard of any cases where governments tried to undermine this by trying a juror for perjury for violating such a pledge.
If you want to argue the morality of breaking your pledge: Everyone tried for a criminal offense has a right to a jury trial - a
real jury trial. It's completely moral to break your silly "pledge" if it means preventing the state from carrying out injustice against a fundamentally innocent person. If a few government stooges are trying to rob you of your power as a juror (and rob the defendant of a real jury trial) merely so they can abuse their own power and unjustly strip someone of their liberty, well...in that case, you have no responsibility to remain honest to them (and if they do their jobs to carry out justice, rather than injustice, then jury nullification won't come into play anyway, meaning you stayed true to your word

). Besides, a [basically] coerced pledge is about as binding as a coerced confession. Sure, you just won't get selected if you don't make the pledge, but no government has the right to corrupt juries by forcing such a pledge on them in the first place in direct contravention of each juror's duty to deliver justice.
The very idea of juries has long been a thorn in the side of government officials and the government itself, and they've long sought to undermine and diminish the vast - and important - power that juries have. The pledge you're talking about is really just a shaming tactic and scare tactic that corrupt (not necessarily by money, but certainly by anti-American ideology) judges and government officials use to discourage and disempower juries. In the legal sense, given the Framers' understand of the word "jury" at the time they wrote the Bill of Rights, denying defendants a real jury trial with such a pledge is blatantly unconstitutional as well. As far as the Constitution of concerned, jury nullification does not undermine the law or create lawlessness; rather, it's a completely intentional check and balance that the people retain.
In other words, if you're made to say a pledge, just say the pledge and cross your fingers behind your back. No judge or lawyer has the right to deny a defendant a trial by jury - and by jury I really mean a jury in the sense that the Framers and all of the classical liberals meant it...a jury with the power to veto unjust laws, not just some disempowered panel of muppet babies.