A U.S. government default (some bills unpaid) looks possible but unlikely. By my count, the topline difference is only about $50B in Nondefense Discretionary spending. Not enough to take the risk of tanking the economy. But there will be plenty of showmanship.

                [$B]    [$B]                GOP      WH     [$B]
               FY2022  FY2023  change    FY2024  FY2024  difference
Discretionary   1,659   1,712   3.2%      1,659   1,712
   Defense        747     792   6.0%        792     792
  Nondefense      912     919   0.8%        867     919      52

A government shutdown (employee furloughs) looks more likely. The longest government shutdowns were in 1995, 2013, and 2018. Congress is now more narrowly split (Senate 51-49, House 222-213), and so reaching a decision will be more difficult. But the longest government shutdown was 35 days from December 22, 2018, to January 25, 2019, and the US stock market did not change much during the previous shutdowns.

days     US        US        US
from  equities  equities  equities
shut    VFINX     VFINX     VFINX
down   sd1995    sd2013    sd2018
-56     33.38    131.99    228.51
-49     32.95    131.86    234.10
-42     33.59    128.67    239.27
-35     33.74    126.99    235.58
-28     34.17    127.78    226.70
-21     34.18    131.27    237.82
-14     34.61    132.95    226.99
 -7     35.22    132.41    224.19
  0     35.17    132.26    208.42
  7     34.92    129.24    214.45
 14     35.18    132.60    218.53
 21     35.23    137.04    224.14
 28     34.40    138.40    230.63
 35     34.98    137.73    230.13
 42     35.53    138.22    233.84
 49     36.37    139.89    234.10
 56     37.57    141.11    240.10

---links---

cbo.gov - Budget Outlook

"There will be some bills unpaid if we do not raise the debt ceiling."
nbcnews.com - Janet yellen early june hard deadline debt ceiling

"We recommend that corporates begin to discuss contingency plans for a U.S. government default with their boards of directors."
clearygottlieb.com - Corporates face novel greater risks from debt ceiling impasse even if no occurs

vox.com - Government shutdown history clinton obama explained

"Shutdowns of the type experienced by the United States are nearly impossible in other forms of government:
Under the parliamentary systems used in most European and Asian nations, stalemates within the government are much less likely, as the executive head of government (i.e. the prime minister) must be a member of the legislature majority, and must maintain the approval of the legislature to remain in power (confidence and supply). Typically a legislature is suspended if a budget fails to pass (loss of supply), and the head of government must resign. Then the head of state may either appoint another member of legislature who can garner majority support, or dissolve the legislature and conduct fresh general elections.
In other presidential systems, the executive branch typically has the authority to keep the government functioning even without an approved budget."
en.wikipedia.org - Government shutdowns in the United States

The United States federal government shut down from midnight EST on December 22, 2018, until January 25, 2019 (35 days) was the longest government shutdown in history.
en.wikipedia.org - United States federal government shutdown

"Republicans want to roll back next year's spending to 2022 levels, but the White House has proposed keeping 2024 the same as it is now, in the 2023 budget year. Republicans initially sought to impose spending caps for 10 years, though the latest proposal narrowed that to about six. The White House wants a two-year budget deal... GOP lawmakers are also seeking cuts in IRS money and, by sparing Defense and Veterans accounts from reductions, would shift the bulk of spending reductions to other federal programs. The White House has countered by keeping defense and nondefense spending flat next year,"
apnews.com - Debt limit biden mccarthy spending cuts