You set the coverage limits you require, often the number your own insurer or lender asks for. A vendor whose recorded coverage falls below one of them cannot propose on your work until it is raised.
You enter those figures once, per trade, and mark each line required or preferred. A company carrying less than a figure you made required is stopped when it tries to answer, and it is told the shortfall in dollars, so it knows exactly what it has to raise rather than being told it did not qualify. A line you marked preferred is reported to you and lets the company through.
Nothing carries a default figure. The number a district asks for and the number a city asks for are not the same number, and inventing one on your behalf would be the most expensive kind of helpful.
Before a price, not after it
general liability and workers’ compensation are read by a person before the company can answer you at all.
So the prices on your desk in March are prices from companies that were already clear. There is no separate week in May where somebody discovers the one you liked cannot show a current certificate.