This question came up in the Volokh Conspiracy forum.
The answer is no. Here is my comment:
The Constitution nowhere provides that a simple majority, either of the body or those present, is sufficient to pass a bill. What it does provide:
- That the House have “Power of Impeachment”, but nothing on a voting rule.
- That that state legislatures “chuse” U.S. senators. No mention of by what vote.
- That the Vice President shall have a vote if the Senate is “equally divided”, but not when if ever they might be equally divided.
- That each house shall “chuse” their officers, but no mention of by what vote.
- Senate requires 2/3 of members present to remove on an impeachment.
- Majority of members of each House to be a quorum, but nothing about voting rules for business, except as provided for specific kinds of issue.
- Submajority may adjourn or compel attendance.
- Each House may determine its own rules of procedure, but does not specify by what vote rules are to be adopted, amended, etc.
- 2/3 of members of a House required to expel a member.
- 1/5 of members present may require a record vote in either House.
- 2/3 of members of each House required to pass bill over a veto.
- 2/3 of Senate members present required to consent to treaties.
- 2/3 of members of each House required to propose amendments.
- 2/3 of state legislatures required to propose amendments or call constitutional convention.
- 3/4 of state legislatures or conventions required to adopt amendments.