The “gang of eight” senators rolling out a bipartisan immigration overhaul this week are gearing up for the battle to formally be joined at the Senate Judiciary Committee and ultimately on the floor this summer.

The senators are expressing optimism that a bill resembling their package will ultimately become law, and President Barack Obama reiterated on Tuesday his commitment to getting a deal passed.

Sens. Charles E. Schumer, D-N.Y., and John McCain, R-Ariz., briefed Obama at the White House on Tuesday about the group’s immigration compromise. They spoke with the president about the trigger in the bill, which Obama does not like but which McCain and Schumer believe is essential to not only passing a bill but getting public support.

After the meeting, the senators exuded confidence that some form of the package will become reality. Schumer said Judiciary hearings will begin Friday and that the bill could be on the floor in late May or June.

Even Senate Minority Leader Mitch McConnell, R-Ky., sounded optimistic.

“We’ll have an opportunity to take a look at it, and hopefully it’ll provide a bipartisan way forward on a very important issue to the country,” McConnell told reporters Tuesday.

Still, the immigration stakeholders acknowledge that no shortage of potential pitfalls remain. At the same time, all are aware of the “now or never” sense of urgency that surrounds the issue and have raw memories of the last effort collapsing in 2007.

“If we fail this time, I don’t know when anybody would take this up. I mean, I said last time this was the last best chance in a decade. This may be the last chance forever,” gang of eight Sen. Lindsey Graham, R-S.C., said Tuesday. Here are just eight of the potholes that lie ahead for the immigration bill:

1. Congressional Budget Office Scoring

The recycling bins of Senate history are filled with well-intended bills that ran into trouble when scored by the CBO. While among the simplest hurdles, the question of how much a piece of legislation costs might be the most difficult to answer. Senators in the gang of eight say the plan will be budget-neutral, using fees to pay for new spending. “We intend to pay for it with fees and not add a burden on the taxpayers,” McCain said.

2. Will the Enforcement Really Happen?

While Sen. Jeff Sessions has been the most persistent Senate critic of the group’s work, his point about enforcement within the borders of the U.S. might carry weight. “The promises in the future, even if it goes into law, of enforcement, haven’t occurred in the past,” the Alabama Republican told reporters Tuesday, expressing concern that the benchmarks for immigration enforcement might not be attained. Sessions pointed to the Immigration and Customs Enforcement officers union’s opposition to the Obama administration’s deferred action policy on undocumented individuals who entered the country as children.

3. Provisions for Immigrants Previously Deported

Frequent opponents of broad immigration overhauls are already criticizing language that would allow people who have previously been deported for nonviolent immigration offenses to gain legal status as what the summary calls registered provision immigrants. Rep. Steve King, R-Iowa, highlighted that provision on the House floor Tuesday afternoon, but Graham said any immigrants willing to abide by U.S. rules should be welcomed. “We want people to come back or stay on our terms, not theirs,” Graham said. “If you’ve committed violent crimes or multiple misdemeanors you’re not eligible.”

4. Funding for the Commission

The plan would establish a new bipartisan commission to improve border security if effectiveness of border security in key areas does not reach 90 percent over five years. The commission would hand down recommendations to improve securing the borders, and according to a summary, the bill would actually appropriate up to $2 billion to implement necessary changes. That idea has raised the ire of some skeptics questioning if that could later be undone through the regular appropriations process.

5. Collecting Back Taxes

The proposal requires that individuals seeking legal status repay any back taxes, already prompting some questions in the Senate halls about the investment that would be required to enforce this tax compliance provision, as well as how it might be implemented and if there could be a new paperwork burden on employers. McCain suggested that if people want a path to become citizens, that won’t be at issue. “They have to prove they’ve been here since before Dec. 31, 2011, that’s one way you do that,” McCain said.

6. Poison Pill Amendments

An open amendment process at the Judiciary Committee and on the floor may require Senate supporters to dodge an assortment of poison pill amendments designed to make passing the bill untenable. In 2007, an amendment offered by then-Sen. Byron L. Dorgan, D-N.D., to an attempted Senate immigration overhaul garnered an unusual coalition of supporters including Republican opponents such as Jim DeMint, R-S.C. The amendment pertained to the future flow of immigrants, an issue that was addressed during the negotiations that led up to the release of the new bill from the eight senators.

7. Getting Both Parties on Board

“It’s not just about the eight of us, if we can’t sell it to a majority of our conferences, then maybe it’s a product not worthy of having been passed,” Graham said. He was making the point that an ideal product would have broad support from Democratic and Republican conferences in the Senate, rather than being the sort of bill that just barely clears the 60-vote hurdle needed to break an expected filibuster. The Republican members made a pitch to members of their conference Monday evening, drawing encouraging words from McConnell and others.

8. And Then … There’s the House

Suppose the Senate ultimately passes an immigration bill with somewhere around 60 votes. As with the gun legislation, the GOP-led House might have little incentive to take up anything similar to the Senate bill. House Judiciary Chairman Robert W. Goodlatte, R-Va., has signaled he may move immigration legislation via a piece-by-piece approach, rather than an all-encompassing measure favored by the Senate group.

Steven T. Dennis contributed to this report.