Most likely, if lying to police or obstructing an investigation, the offense charged would a variation of making a false statement to law enforcement under 750.749c. This law states:
(1) Except as provided in this section, a person who is informed by a peace officer that he or she is conducting a criminal investigation shall not do any of the following:
(a) By any trick, scheme, or device, knowingly and willfully conceal from the peace officer any material fact relating to the criminal investigation.
(b) Knowingly and willfully make any statement to the peace officer that the person knows is false or misleading regarding a material fact in that criminal investigation.
(c) Knowingly and willfully issue or otherwise provide any writing or document to the peace officer that the person knows is false or misleading regarding a material fact in that criminal investigation.
As you can see, I have underlined the portion that would most likely be applicable to you. Simply making a statement that turns out to be false is NOT a crime. The statement must knowingly and willfully be false. That means the person who gave information to police must know that the statement is a lie. If the person did not know the statement was a lie, they cannot be convicted of the crime. The state must show, beyond a reasonable doubt, that the statement was made knowing it was a lie. Without any direct evidence of that, it would be hard for them to sustain a charge against you at trial.
So, while there is nothing you can do to "force" someone to accept a plea agreement, if you were charged with providing a false statement to law enforcement, the state would have to show that you knew it was a lie. Without proof that you knew it was a lie, it would be difficult for them to convict you.
Any questions based on what I have provided thus far?