Yes, they absolutely can make him leave, via the 25th. I suspect the House Speaker would cooperate.
given the players, it may be easier to impeach and convict than to 25A
The speaker has very little to do with the process. The way it would work is this:
Harris and a majority of the Cabinet would have to agree to implement the 25th Amendment. They would then have to send a letter to the speaker and the president pro tempore of the Senate informing them that the president is unable to perform the duties of his office. Harris would then become acting President.
Next, Biden would send a letter to the speaker and president pro tem saying he was able to perform the duties of his office, and would immediately resume his his office.
Harris and the Cabinet would have to send another letter to Congress saying Biden was unable to perform the duties of his office. Harris would again become acting president.
Congress would then be required to convene within 4 days for the purpose of settling the matter. They would have only 21 days from the date they receive the second letter from Harris to issue a decision. If 2/3 of each house of Congress do not agree that Biden cannot perform the duties of the office, he resumes his role as president.