The house is the bigger shit show and typically writes the budget bills since the Senate will usually pass it if the house does. (Not 100% accurate , see edit) The Senate did pass their own bipartisan stopgap funding for 6 weeks, but McCarthy refused to even discuss it because it contained funding for Ukraine.
This is yet another one of those things that has no real safeguards because Congress has always passed budgets without much issue for the majority of history. There’s always negotiating, but shutting down the government has always been off the table until fairly recently.
There is a bipartisan bill being proposed to end shutdowns and just fund the government at current levels until a budget is passed. But most members of Congress don’t support it because it means they can’t use the shutdown as leverage, on either side.