Not American here. Isn't Congress controlled by Republicans? If I understand correctly, it would take 5+ Republicans voting against the party line for a Republican bill to fail to pass? Is this common?
For the House of Representatives, the state will hold a special election to fill vacancies:
> When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies.
- Article I, Section 2
For the Senate, the governor of the state may (per their legislative body's approval) make a temporary appointment and will also hold a special election:
> When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.