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.