The phrase "able to commit themselves" is correct and usable in written English.
It can be used when discussing someone's capacity or willingness to dedicate themselves to a task, cause, or relationship.
Example: "The team members must be able to commit themselves fully to the project to ensure its success."
Alternatives: "capable of dedicating themselves" or "willing to invest themselves".
He said he thought about "members of my own staff who are in incredibly committed monogamous relationships, same-sex relationships, who are raising kids together," and about "those soldiers or airmen or Marines or sailors who are out there fighting on my behalf and yet feel constrained, even now that 'don't ask, don't tell' is gone, because they are not able to commit themselves in a marriage".
Obama said he has talked to friends, family, and neighbors about it; hell, he has people on his staff who are gay (surprise!), and it's not fair that they feel "constrained... because they are not able to commit themselves in a marriage".
When I think about those soldiers or airmen or marines or sailors who are out there fighting on my behalf and yet feel constrained, even now that Don't Ask, Don't Tell is gone, because they're not able to commit themselves in a marriage... it is important for me to go ahead and affirm that I think same-sex couples should be able to get married.
Duddy-Burke said Francis' comments suggest that gay and lesbian Catholics are somehow less able than their straight peers to commit themselves to religious life.
Dehumanising treatment makes jailers and torturers able to commit yet worse horrors, once victims no longer look like themselves.
With age, the numbers of unmarried black women and men become significantly lower, suggesting that both find themselves at places in their lives where they are ready and able to commit.
If I love this man, and am able to commit to the idea of being with him, I must take seriously his commitments, and his intentions.
Nick played with Liam because I wasn't able to commit myself to 10 weeks.
"We first of all choose participants willing and able to commit to the 10 weeks.
