This is a rather amusing theory. Somehow, the 14th Amendment makes a debt ceiling illegal! Just one problem: we do not need to assume more debt in order to pay our current obligations. The amount the United States pull in per month is many times the debt that comes due each month. What it does mean, however, is that the government would have to reduce its spending as it has finally run out of money.
Democrats are trying a sleight of hand here. Not paying the debt would be unconstitutional, but it does not follow that a debt ceiling is ergo unconstitutional. We have the money to pay for our debt via taxation; what we don't have is money to pay for all of this other spending the government ought not be bothering with. The Constitution does not require this latter spending, only the prior.
Senator Murray is wrong. The question is about current and future spending. If you reduce that, there is more than enough to pay our constitutionally obligated debt payments without increasing the debt ceiling.