It's not really the case that only the Senate can - it's just that the consequences for the House doing so are unambiguous and well-known, whereas in the case o

It's not really the case that only the Senate can - it's just that the consequences for the House doing so are unambiguous and well-known, whereas in the case of the Senate convention was that it would not do so, so the consequences were unknown. The traditional way for a lower house to register a lack of confidence in the government is in fact to amend the appropriation bills to appropriate one additional dollar from the treasury. A government that no longer controls the treasury must resign or call an election.