From the BBC: What's the 'nuclear option'?
It is a rule change that would allow the budget to pass by a simple majority of 51 votes, rather than the 60 currently required under Senate rules.
The president's fellow Republicans currently have 51 seats in the 100-seat Senate.
But Mr McConnell has repeatedly refused in the past to invoke such an extreme legislative manoeuvre.
A number of Republican senators on Friday made clear their staunch opposition to the "nuclear option".