As for Speaker John A. Boehner of Ohio, no doubt some conservative House members who are eager for another debt limit dust-up are angry with him for allowing the measure to go through without any strings attached. But many others are grateful to the speaker for finding a way to spare them the vote and spare their party another bruising in public opinion polls when Republicans are feeling very good about their midterm election prospects.

Mr. Boehner faces an immediate question. Having again shown a willingness to violate the so-called Hastert rule — the unwritten code that legislation should pass the House only with a majority of the majority — will he now be willing to take a similar approach on other major issues, namely immigration?

After all, he and scores of other House Republicans are interested in overhauling the nation’s immigration policy, and Mr. Boehner could easily shape a significant bipartisan majority if he teamed up Republicans who are willing to act on immigration with Democrats who are clamoring to do so. Democrats have encouraged him to just put a Senate-passed bill on the floor and pass it with mainly Democratic votes, as he did with the debt ceiling increase.

But that is unlikely to happen. Mr. Boehner is no fan of the Senate plan, and he would like the House to act on a series of immigration-related proposals rather than one sweeping bill like the Senate did. But another significant reason immigration legislation will not get the same treatment as the debt limit bill is that Republicans see no deadline or looming crisis that will force the issue.

If advocates of immigration changes want Mr. Boehner to plunge ahead, they may need to amp up the pressure.

For the most part, Mr. Boehner has turned to Democratic votes when he has exhausted other options and faced a potential catastrophe like running off the fiscal cliff. He did allow a renewal of the Violence Against Women Act to pass with predominantly Democratic votes, but House Republicans had earlier advanced their own version. In all previous cases, the number of Republicans joining Democrats was well over 28 — 87 Republicans in the violence against women bill.

Recent comparable episodes brought to mind by this week’s House vote were the 2002 vote to overhaul campaign finance laws. Just 41 of Republicans in the majority — 18 percent — sided with most Democrats to pass that landmark legislation. It was opposed by the House leadership, but enough Republicans joined with Democrats on a petition to force it to the floor, setting off a fevered debate.