Suppose that for some reason, the House of Representatives wants to stop the Senate from doing anything. Could they accomplish that by passing hundreds of frivolous bills, so the Senate would be stuck wasting time voting on those bills? Of course, the House couldn't do anything else during this time either.
In other words, can one house of Congress run a denial of service attack against the other house by flooding them with bills?
No, because neither House nor Senate is obliged to consider each and every bill brought to it.
The Constitution of the United States allows each house of Congress to make their own rules for their proceedings (Article I, Section 5, paragraph 2.) Neither has any control over the other's rules. Neither is under any obligation to consider or vote any bill beyond what their own rules require and they can change their rules when they want without any input from the other house.
It's actually quite routine for both the Senate and the House to just completely ignore bills passed by the other, especially when they're not controlled by the same party. Both major parties in both houses frequently pass legislation that they know the other would never even consider just for political optics, especially when one party controls the House and the other controls the Senate. This allows the party controlling the chamber that passed the bill to campaign on
See?! The Other Party didn't even consider the Saving Cute Puppies From Brutal Massacre Bill [which, of course, actually had nothing to do with puppies and instead accomplished nothing or some nonsense partisan purpose] that we passed! We need control of the Other Chamber in order to pass this important legislation and save the puppies!
when the next election season rolls around.
So, in short, no, they can't do that because the House has no mechanism to force the Senate to vote on anything (and vice versa.)
The Speaker of the House and the Senate Majority Leader set the agenda for items to be brought to the floors of their respective chambers. Either is free to ignore proposed legislation from the other institution.
No, but, interestingly enough, the House of Representatives can do the exact opposite—force the Senate to stay in session—and often has.
Article I, Section V, clause 4 of the Constitution says (emphasis added)
Neither House, during the Session of Congress, shall, without the Consent of the other, adjourn for more than three days, nor to any other Place than that in which the two Houses shall be sitting.
They can’t force the other chamber to do anything, but this still matters, because Article II, Section II says (emphasis added)
The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.
So, when the President’s party controlled the Senate, but not the House, from 2011 to 2014, the majority party in the House would show up, hold a short pro forma session every three days, and go home, just so the Senate could never go into recess and allow the President to make any appointments.
In 2014, the Supreme Court ruled that the President cannot make a recess appointment during a recess that lasted only three days. Because gridlock had never escalated to that point before, the Court had never previously needed to rule on this.
As GS noted in a comment, the majority in the Senate was not large enough to break a filibuster (which is not in the Constitution, and was not routinely invoked on all bills and appointments until very recently) or they could have confirmed the President’s appointments the regular way.
