Question

After the idea arrives to the senate, who is it assigned to

Answer 1

If you are talking about a bill, it is debated with the House of Representatives, and then sent to the President for signature.

Answer 2

If you mean bills ,Generally, bills are legislative proposals that, if enacted, carry the force of law, whereas resolutions do not. Though, this is not always true. ... A Bill starts either in the House of Representatives or in the Senate. Bills that start in the House are designated “H.R.”