You are right that the Constitution is clear about revenue legislation but does not directly address appropriations, or spending, measures. Extending the House's right to originate to the spending category has been a matter of long dispute between the House and the Senate. The Senate has repeatedly asserted its right to originate spending legislation, adopted resolutions to that end, even called for commissions to study the dispute. However, the House has a different perspective. House precedents have defined "revenue measures" to include general appropriations bills, claiming that at the time the Constitution was adopted, "raising revenue" meant "raising money and appropriating the same."

So, whenever the Senate does initiate appropriations legislation, the House practice is to return it to the Senate with a blue piece of paper attached citing a constitutional infringement of House prerogatives. The practice of returning such bills and amendments to the Senate without action is known as "blue-slipping."

Without House action, Senate-initiated spending legislation cannot make it into law. So in practice, the Senate rarely attempts to initiate such bills anymore, and if it does, the House is diligent about returning them. Regardless of one's opinion of the correct interpretation of the Constitutional provision, the House refusal to consider such Senate legislation settles the matter in practice.

However, just as is spelled out in the Constitution for revenue bills, the Senate right to amend appropriations bills received from the House is not disputed. As with all legislation, a House-Senate conference will have to come to terms with the differences between the two versions of an appropriations bill. Each chamber will have to adopt the compromise conference text. So in the end, the process gives the Senate an equivalent role to the House in determining the text of both revenue and appropriations bills.

One can argue over how much influence the power of origination actually has. It sets the initial framework, which means deciding which matters to include and which to leave out. At times, the House debate and amendment process may build some political momentum which the Senate may find difficult to ignore. On the other hand, while the Senate cannot vote first on a revenue bill, and by extension, an appropriations bill, and send it to the House for legislative action, there is no restriction on the Senate's consideration of such measures before the House has acted.

The Senate need not wait for the House papers to come over before starting legislative consideration of revenue or spending bills, unless it so wishes. To save time, the Senate often will process their own bills through committee, and even debate and amend them on the floor. It completes all the legislative stages up to the vote on final passage of the Senate-numbered measure. The legislation is then held until the House version comes over. The Senate proceeds to amend the House version to reflect the text of its own product, then passes the amended House bill, and returns the revised measure to the House. This practice provides the Senate with the opportunity to make legislative progress on spending and revenue measures even if the House has not yet completed work on them.