In my opinion, this is a mostly empty threat. The President has virtually no official power over members of Congress. Article I, Section 5 of the US Constitution gives the power to discipline members to the Congress itself. Section 6 gives members of Congress a wide range of protection against harassment by the executive. Short of prosecuting serious criminal charges against them (for which he'd need to have actual evidence), there isn't anything a President can do to target individual members.
Unofficially, the President has more options. The biggest lever that a President has is that normally he is the head of his party. That means he can have a great deal of influence over the allocation of party resources. Many members of Congress, particularly members without much seniority or those from small districts, rely on support from the party coffers for their reelection efforts. Threatening to withhold that support, usually during the primary election, can be an effective way of motivating members to fall in line. However, this particular President's relationship to the Republican party is more distant than usual. He will likely have trouble persuading party leadership to go along with such sanctions, especially because party leaders are all too aware that these kinds of internecine fights can backfire, possibly resulting in the party losing the seat.
Alternatively, the President could try to back a primary challenger himself, perhaps by actively campaigning on their behalf. This might be an option for targeting a single, particularly hated, foe in Congress (it wouldn't surprise me to see him target the Speaker this way), but it would be hard to do this in a few dozen races around the country. Late-night tweet storms notwithstanding, winning a primary election against a better funded, better organized opponent requires a sustained effort, and each race requires a message tuned to its voters. Keeping that up for months on end in more than a couple of races would paralyze the administration. The President might be able to get grassroots organizations to do the heavy lifting for him, but it's not clear that these members' decision was especially unpopular among their constituents, so rallying grassroots opposition will be harder than it was in past years, when merely being seen as cooperating with President Obama was seen as a betrayal.
If neither of these avenues is likely to work, then the President is left without much recourse beyond slagging off House members off on Twitter. I don't think most of them are too worried about that. To be in Congress you have to develop a pretty thick skin because there is always someone mad at you. You also have to learn to deal with hecklers because, again, there are always some that show up. (See, for example, Senator Lindsey Graham's performance at one of his recent town halls.) Twitter attacks aren't likely to worry members of Congress unless it looks like there is a real chance that they will mobilize a public backlash. Since most of the Republicans who defected on this vote did so precisely because they had a better sense of where the public stood on this bill than the Administration or the House leadership did, that doesn't seem too likely.