Something of a paradox, isn't it? The motto first appears on the two-cent coin in 1863 as a means to curry support behind the Union's failing effort to maintain itself. Had the Union collapsed, then the constitution underwriting it would become irrelevant. So in a sense, originally, it would have been rather like saying, "I like the US Constitution, but support actions that may lead to its failure." Or kinda like pointing out, as StatesRights often and rightly does, that Lincoln's suspension of habeas corpus and such was unconstitutional and tyrannical. Yet without the tyranny, the union may well have decayed, then the question of what is and isn't constitutional becomes irrelevant.
To more relevant points: Note that Article I Section 8 delineates the Power of Congress, and reads, in part, that congress has the authority "To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;"
So you can reasonably assume that the framers wanted the congress to be in control of the printing of the money, deciding what denominations would be available, etc. You could perhaps even argue that they intended for the congress to oversee the design of the money. And the designs they settled on have various mottoes including "Liberty" and "In God we Trust." Thus it seems expressly constitutional.
That said, I never liked it on the money. For various reasons. Some will view "god" as a particular god, favored by congress, and may feel alienated by its inclusion. As an immigrant nation we should avoid alienating new arrivals. Some observant, monotheistic types may find it profane and offensive to call upon the god to bless the money. It also seems a bit dated in this day and age of reason and enlightenment, to encourage at taxpayer expense the intervention, or invention, of gods. At any rate, if you really believe in fiat money, then why would need any god's blessing on the money? But whether or not I like the motto, I'd have to say that since it doesn't actually prohibit religious freedom, nor establish a state religion, it doesn't violate the Bill of Rights. Combine that with the specific authority of congress to make money, then you have a hard time eradicating it based on some notion of its dubious constitutionality. So I voted Yes(I/O).
Bear in mind that simply taking a pen and crossing out the offending motto on your bill does not render it "unfit to be reissued," so there's no violation of United States Code Title 18, Part 1, Chapter 17 if you want to ease your conscience by obliterating the motto. Similarly, writing "Allahu Akbar" or "I'm saved, how 'bout you?" or "Om Mani Padme Hum" on a bill doesn't violate the law either. Just have fun with it. After all, the government is considering much more wasteful projects at the moment than using more ink than is necessary on bills, so the umbrage might be better channeled elsewhere. Just a thought.