As a rough cut, these would offset each other, so there would be no net increase in costs or spending, it would simply get shuffled around. The money spent on health insurance would instead become a tax, and the insurance co spending on health care services would become government spending on health services.

In reality, there should be some overall savings, as insurance co profits come out of premiums. And there might be some minor savings elsewhere in administrative costs.

Right now, most Americans are ensured by their employers. When the employers stop paying the premiums, they're not going to suddenly increase the salaries of their workers by x% to offset the savings. They'll just dump the benefits.

Let's look at some numbers. California floated Assembly Bill 1400 (California Guaranteed Health Care for All Act) in 2022. It carried a price tag of $400 billion.
legalclarity.org - Californias single payer healthcare status and challenges

California had ~39 million people in it in 2022. That works out to $10,256 per person.

Later estimates on another form of the legislation pegged the cost at more like $500 billion:
trackbill.com - Assembly appropriations

The analysis estimated that with no changes, total health care spending would be $517 billion in
2022. The following are example scenarios and associated total spending estimates:
1) No cost sharing, direct payments to providers, and no LTSS expansion: $501 billion ($16
billion savings over status quo).
2) Income-related cost sharing, no LTSS expansion: $482 billion ($35 billion savings compared
to status quo).
3) Income-related cost sharing, LTSS expansion: $508 billion ($9 billion savings compared to
status quo).
4) Including an intermediary increases estimated spending for the above scenarios by $4 billion
to $5 billion.

At $500 billion and with CA's population of 39.4M, that's $12,690 per person and a national commitment of $4.3 trillion.

Single payer health plans by themselves won't work with health care service priced as it is today; more reforms would be needed.