Speaker John A. Boehner looked to shore up his right flank Wednesday ahead of a looming battle over immigration as the Senate lurched its way to the finish line.

The Supreme Court, meanwhile, gave the issue a lift by taking the thorny issue of gay rights off the table, while advocates continued to march on Congress and demand action.

Boehner’s Pledge

The Ohio Republican reaffirmed his commitment to House Republicans on Wednesday that he would not bring up the Senate bill for a vote in the House. While that bill has significant Republican support — and seems certain to get close to 70 votes on final passage — it has also faced a sizable backlash among parts of the party’s base.

According to a source in the room, Boehner told lawmakers Wednesday morning that the House would do its own bill “through regular order and it’ll be a bill that reflects the will of our majority and the people we represent.”

Boehner referred to a letter from himself and other GOP leaders that said the House would not take up a Senate-passed immigration bill. It’s still not clear how the House will bring up its own bill. Bringing smaller, individual bills to the floor could allow the House to pass the most popular immigration measures among Republicans, leaving the tough issues to a conference with the Senate. The way ahead will depend on the response members get when they return to their districts next week for the July Fourth break.

No Clear Path

Rank-and-file members predicted an unsteady ride ahead.

“If you insist on no compromises from the ‘gang of eight,’ yeah, they’re not going to get it done,” said Matt Salmon, R-Ariz. “If you’re earnest, then you’re saying, ‘We’re willing to come up with a solution, but we’re not going to give the store away.’ We’re not going to do something that we believe is bad policy just to get votes in the next election.”

Salmon has led an insurgent effort to codify the “Hastert rule” setting a “majority of the majority” requirement for bringing legislation to the floor.

Rep. Tom Cole, R-Okla., predicted the immigration timeline could slip behind looming budget battles.

“I wouldn’t be expecting us to vote on immigration by the end of the year, if not early next year,” Cole said. He said he did not see how a “a big immigration brouhaha” would help the House deal with more immediate concerns, such as averting a government shutdown and dealing with the debt ceiling. Hispanic Rep. Raúl R. Labrador, R-Idaho, who walked out of House compromise talks after months of negotiations, said the GOP would lose in the next elections if it tried to “buy votes” with an immigration overhaul.

“Because we’re going to lose on policy and we’re going to lose politically,” Labrador said. “Democrats are always going to be willing to give more than we are, because they’re always willing to pander more than Republicans are willing to pander.”

Labrador predicted that Boehner would not use the piecemeal approach, saying he thought all the bills would be joined in the end.

Senate Logjam

The Senate, meanwhile, remained on track to finish up its bill by the end of the week but struggled to reach a deal on amendments, which could determine the final tally. Judiciary ranking member Charles E. Grassley, an opponent of the gang of eight immigration plan, blocked an effort by Senate Majority Leader Harry Reid, D-Nev., to set up a “vote-a-rama” with 32 amendment votes.

“They don’t want to take tough votes, so they’ve chosen just a few of our amendments to make it look like it’s very accommodating. So, I have to say I feel a bit used and abused in this process,” the Iowa Republican said.

Gang of eight Democrat Charles E. Schumer of New York was quick to suggest that the Republican objection came about in a bid to block a vote on an amendment backed by Sen. Rob Portman, R-Ohio, to enhance the E-Verify system for employment status verification.

Portman’s amendment could have been included as part of a bipartisan catch-all package that won adoption earlier Wednesday, but he reiterated on the floor Wednesday he wants a separate vote to signal the importance of the provision. And his vote appears to hang in the balance.

The Senate earlier adopted, 69-29, an omnibus amendment Wednesday that incorporated strengthened border security provisions and limited debate on the Judiciary Committee’s substitute, 67-31. Absent a deal, a vote to limit debate on the underlying bill will take place Thursday, with a vote to pass the bill no later than Friday afternoon.

Supreme Help

The Supreme Court’s decision to toss out the Defense of Marriage Act removed another contentious issue from the immigration debate. Judiciary Chairman Patrick J. Leahy, D-Vt., has authored an amendment regarding immigration benefits for married same-sex couples.

“With the Supreme Court’s decision today, it appears that the anti-discrimination principle that I have long advocated will apply to our immigration laws, and binational couples and their families can now be united under the law,” Leahy said.

One More March

While lawmakers maneuvered inside the Dome, marchers were chanting outside. The message was simple: “We are current voters, we are future votes, and we will vote.” The warning was clear, as they went by the Republican National Committee headquarters and the headquarters of the National Republican Congressional Committee as well as the Capitol.

Emma Dumain contributed to this report.