
The government shutdown is BECAUSE we cannot reconcile the budget. This literally falls into that category. The government shuts down when the allotted budget period elapses without an agreed upon replacement or a continuation. So to end the shutdown, they have to reconcile the budgetary disputes between the two parties.
The Senate typically requires 60 votes to invoke cloture on an issue (end debate and bring the issue itself to a vote). However, the Senate can circumvent this rule by a majority vote but it is considered bad form in what is supposed to be a collaborative and bipartisan chamber. In 2013 Harry Reid did this with judicial nominees to prevent all of Obama’s judicial appointees from being blocked by McConnell and the Republicans, but did not include SCOTUS nominees, I.e. those still required a…
60 vote supermajority. In 2017 McConnell expanded this to SCOTUS nominees to allow the confirmation of Gorsuch and later Kavanaugh and Coney-Barrett. Circumventing the rule around cloture for all legislation is something that they could do in theory, but neither party is likely willing to go that far because it makes the minority party completely powerless in the Senate, and no majority holds forever.