When people complain about the filibuster rules in the Senate, they often seem to assume that the only remedy involves jawboning that body to change its rules. There’s nothing else that can be done, right?
Wrong. There are many ways of putting institutional pressure on the Senate. With respect to executive appointments, the President could start recess appointing everyone. This would not solve the problem of invoking cloture or “holds” entirely, but it would diminish the Senate’s power.
More interesting is the thought that the House of Representatives can take unilateral action to make the Senate’s life difficult. Here’s a famous example. Until 1871, agreements with the Native American Tribes took the form of treaties that were ratified only by the Senate. The House grew more and more critical of this regime over time, in part because they were excluded. So they just stopped appropriating money for these treaties until the Senate agreed that tribal agreements should be approved by a majority of each House, rather than by 2/3 of the Senate. It took a few years, but the Senate finally caved in.
Similarly, in the 1940s the House wanted a share of major foreign policy decisions. So they passed a constitutional amendment (with the tacit support of FDR) ending the Senate’s monopoly over treaty ratification and put the Senate on the spot to vote yea or nay on that proposal. Rather than campaign defending its exclusive authority, which was by then rather unpopular, enough Senators caved and a much broader use of “executive agreements” became the norm.
Today the House could pass a constitutional amendment ending the filibuster and make Senators defend that practice. Or they could start refusing to fund, for instance, any earmarks for Senators who support the filibuster as it currently stands. It’s just a question of whether the political costs are worth incurring.