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Good Tuesday morning from Washington, which will be analyzing the nuclear deal the Obama administration just made with Iran. The deal comes as President Obama is scheduled to deliver a big speech, while on the campaign front, Gov. Scott Walker, an opponent of the Iran deal, has joined the crowd running for the Republican nomination. But first, Hillary Rodham Clinton will be returning to the Capitol to court a group she was unable to win over in 2008.

Mrs. Clinton will visit Capitol Hill on Tuesday for a private meeting with Representative Nancy Pelosi, the minority leader, and then a series of events with congressional Democrats — a group that did little to help her in 2008, but that is now greeting her with open arms.

Mrs. Clinton will sit with Ms. Pelosi ahead of a meeting with the Democratic congressional caucus. She’ll also attend a weekly luncheon for Senate Democrats — including Senator Bernie Sanders, the Vermont independent who is challenging her for the Democratic presidential nomination.

And there will be smaller meetings with basically every subset of the caucus — the Congressional Black Caucus, the Hispanic Caucus, and the Asian-Pacific Americans Caucus.

For Mrs. Clinton, the meetings highlight the degree to which her second presidential campaign is aggressively reaching out to those who did not support her last time around. A star senator from New York in the 2008 campaign, Mrs. Clinton was viewed with suspicion and some hostility by some of her colleagues, some of whom served as early supporters of Senator Barack Obama, then her rival.

Eight years later, Mr. Obama has been derided for having a weak relationship with congressional Democrats, who now are embracing Mrs. Clinton. Ms. Pelosi was among the first elected officials to voice support for a second Clinton campaign, well before it was a certainty.

There are also a number of new faces on the Hill, giving Mrs. Clinton new opportunities to find support.

Maggie Haberman

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The political world is likely to be consumed by the deal Iranian and American negotiators made to curtail Iran’s nuclear abilities in return for the lifting of sanctions against the country. Republican presidential candidates generally vigorously oppose any deal, while Senator Rand Paul of Kentucky has expressed support for talks with Iran. The Democratic candidates are generally supportive of the Obama administration’s approach.

Martin O’Malley, the former Maryland governor who gave a well-received speech on Monday to the National Council of La Raza, a Latino civil rights group, will unveil his immigration platform.

And, though it is slightly outside the world of politics (by about three billion miles), the New Horizons spacecraft will make its closest approach to Pluto around 7:50 a.m. Eastern time after a journey of eight years, and will record close-up images of a onetime planet whose appearance we know nearly nothing about.

After months of behind-the-scenes talks and a high-profile move by Mr. Obama to commute the sentences of nonviolent federal drug offenders, criminal justice overhaul appears poised to have its moment this week.

In a speech to the N.A.A.C.P.’s annual convention in Philadelphia on Tuesday, Mr. Obama will lay out his vision of how to tackle the issue, embracing initiatives, including revamping criminal sentences, that have garnered support from Republicans and Democrats.

“We’re at a moment when some good people in both parties — Republicans and Democrats and folks all across the country – are coming together around ideas to make the system work smarter, make it work better, and I am determined to do my part wherever I can,” Mr. Obama said in a video the White House released on Monday, as he commuted the sentences of 46 inmates, the most in a single day since President Franklin D. Roosevelt. That brought his total number of commutations to 89, the most by any president since Lyndon B. Johnson.

Calling for action by Congress this year, Mr. Obama will urge an end to “unwarranted disparities and unduly harsh sentences,” a White House official said, arguing that change was needed to promote fairness, protect the public and make better use of limited funds. He will follow up the speech with a trip on Thursday to El Reno Federal Correctional Institution outside Oklahoma City, becoming the first sitting president to visit a federal prison when he meets with inmates and law enforcement officials there.

Mr. Obama’s full-throated entry into the debate may be a catalyst for action on Capitol Hill, where Republicans and Democrats supporting an overhaul will come together just as the president is speaking on Tuesday to have a public conversation on criminal justice.

— Julie Hirschfeld Davis

Senator Mitch McConnell of Kentucky, the majority leader, will take a two-year highway bill to the Senate Republican Conference on Tuesday, hoping to get quick agreement on a plan just big enough to get the infrastructure hot potato off Republican plates until after the 2016 election.

He faces opposition from an unlikely opponent: Representative Paul D. Ryan of Wisconsin, chairman of the House Ways and Means Committee.

The big question is how Mr. McConnell plans to pay for a bill that could cost more than $20 billion. Republican leaders are adamant that they will not go the route that business leaders, union bosses, some Democrats and a few Republicans want: an increase in the federal gas tax.

Mr. Ryan is pressing for an $8 billion measure to keep the highway trust fund running on fumes just through the end of this year. That, he reasons, will keep pressure on Congress to pass a broad business tax overhaul this year that he hopes would fund a multiyear infrastructure bill – a desire shared by Mr. Obama.

Mr. McConnell, however, thinks that’s a pipe dream.

Others are looking at the fight and shaking their heads. Representative Earl Blumenauer, Democrat of Oregon, says the answer is staring them in the face. A 15-cent-a-gallon increase in the gas tax, he argues, could fund a six-year infrastructure bill that would reap enormous economic benefits while providing certainty to the Transportation Department’s long-term projects.

— Jonathan Weisman

Mr. Walker, who built a national conservative following by crippling public employee unions and then defeating an effort to recall him, announced on Monday that he was running for president as a Washington outsider who would reduce taxes, challenge Iran and Russia and cut the size of the federal government.Here is a look at where he stands on crucial issues and what his path to the presidency might be.

Senator Marco Rubio of Florida has started his presidential campaign on strong financial footing, raising about $12 million since announcing his run in April.Mr. Rubio is one of several candidates who have released their totals ahead of the Federal Election Commission’s first filing deadline on Wednesday.

And in a speech in New York, Mrs. Clinton called for tax relief for middle-class families, an increase in collective bargaining, and other incentives to raise wages for the group.

The early success of Mr. Sanders, Politico writes, has surprised even his colleagues.

Representative Steve King, Republican of Iowa, defended Donald J. Trump and his comments on Mexican immigrants. Mr. King said those comments were “catching fire” with voters, National Journal paraphrased, and that “if the caucus were held today, he’d probably come out on top.”

And journalists at The Milwaukee Journal-Sentinel, who have spent more time covering Mr. Walker than most, live-blogged his announcement.

Some of Senator Ted Cruz‘s colleagues, including Mr. Paul, are upset about how they are portrayed in Mr. Cruz‘s new book, Politico reports.

It was Rick Santorum’s turn to take the Trump litmus test on Monday, and he took a different approach than some of his rivals running for president.

Like some of his colleagues, Mr. Santorum said he appreciated that Mr. Trump had highlighted such an important issue as immigration and then suggested that he might have phrased things more artfully than saying Mexican immigrants were mostly criminals and rapists. Then Mr. Santorum said Mr. Trump, a billionaire businessman, was not sufficiently conservative on the issue.

“He may be good on the border,” Mr. Santorum said at a breakfast hosted by The Christian Science Monitor. “But on other issues, he’s not all that conservative.”

Despite calling for the construction of a big border wall that Mexico should pay for, Mr. Trump has suggested at times that immigrants living in the country illegally should have a pathway to citizenship. Mr. Santorum, a former senator from Pennsylvania, is against such a path and suggested that Mr. Trump is actually too lax on immigrants who come to the United States illegally.

“All that glitters is not gold,” Mr. Santorum said.

— Alan Rappeport