It's still majority consent in terms of voting. The point about depth of support is to point out that just because >70% of people support a given item on polls does not mean it'll translate into action at the ballot box. To re-use the earlier example: most Democrats would take a candidate that's pro-gun, pro-choice, in favor of higher marginal tax rate over a pro-life, anti-tax candidate that supports tougher gun control. The depth of support for gun-control is shallower than the depth of support for other issues. Conversely, most anti-gun-control voters will never support a pro-gun-control candidate even if they agree with them on many other issues - they'd prefer an anti-gun-control candidate even if they diverge on other issues. Depth of support is high. Thus, gun-control doesn't get passed because plenty of people who would prefer gun control still consent to anti-gun-control candidates because they prioritize other issues.

The idea is that claiming consent of the majority doesn't exist because initiatives that score high on polls don't get implemented by government is highly naive. People can, and do, consent to policy they don't agree with if it's in pursuit of other things they value more deeply.