Article 2, Section 3 of the constitution details the two things a President can force Congress to do (emphasis mine):
He shall from time to time give to the Congress Information on the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
And that's all he can do. He can say "hey, I think we urgently need to deal with X, so I shall convene you to do so", but the Houses are under no obligation to do anything other than to convene and hold session. They aren't even obligated to talk about the issue. They can simply convene the session, decide there's nothing they need to do, and then close the session immediately afterwards.
The adjournment power has never been exercised to date, but the convening one has. In the modern operations of the Houses both powers are minor to irrelevant anyway. You may have heard the adjournment clause get brought up recently, but merely as a proposed tactical move involving an intentional failure to agree by the House, all so the President could then shove in some recess appointments past an uncooperative Senate.
Originally the travel time between the capital and where the various Congressmen resided was substantial. Indeed, "Congressman" was originally expected to be a side gig that you did in addition to more traditional work, not a well-paying, all-year-long time-consuming career of its own. As such it was expected that Congress could and would not be in session for months at a time. But the founders knew something urgent could happen during that span, or any other span when Congress was adjourned, so they made sure the Executive had the power to pull Congress back into session.
Other than that, the President's sole power over Congress is political in nature. We have seen President Trump, for example, wield his political influence to undercut the re-election campaigns of (Republican) Congressmen who do not 100% support him, to varying degrees of success. Given that the House is currently under Democratic control, however, he is unlikely to be able to force his way on the matter. Best he could do is try to jeopardize some other piece of legislation and offer up not doing so as his concession for the House doing the other thing he wants (budget laws are modern day favorites, with government shutdowns becoming somewhat regular as a result). However, it is hard to imagine this particular matter as being something the House Democrats won't be completely resistant to.