Moments like these I wish there was a no-confidence mechanism in U.S. government. I mean, one that actually works in a timely manner, unlike impeachment.
Even a no-confidence motion wouldn't help in this case because his party has a majority of seats in both houses. No-confidence motions only work if the government has a plurality of seats but not a majority.
Oh, in parliamentary systems majority parties can and will get rid of leaders if there is enough internal discontent - that's how Thatcher fell from being PM, for example, or how Abbott fell recently in Australia, etc.