Yes, that’s the nature of how the Senate has worked at least the last 50 years. If you want a bill to pass, you need to propose one that’s going to get 60 votes. And it’s up the majority party to propose that bill, since the majority leader by and large controls what bills make it to the floor.
Bringing a budget bill that doesn’t have 60 votes and then refusing to negotiate isn’t members of the minority party failing to come to the table, that’s the majority party failing to govern.
The majority gets to block any bill they want by not bringing it to the floor. The minority can only block bills by not allowing them to get to 60 votes.
Budgets are a little different, since you kind of have to pass one to have a functioning government — so you need to build a 60 vote coalition, and since the majority proposes the bill it’s up to them to offer a budget that builds that coalition.
Bringing a budget bill that doesn’t have 60 votes and then refusing to negotiate isn’t members of the minority party failing to come to the table, that’s the majority party failing to govern.