Trump swept the Republican primaries in five East Coast states on Tuesday, while Clinton won in Pennsylvania, Maryland, Connecticut and Delaware, dropping only Rhode Island to Bernie Sanders

It's still only April, and their opponents swear they're not going anywhere. But Trump and Clinton both used their victory speeches to pivot towards the general election , giving a preview of the clash we might see between them over the next five months.

Here are five takeaways from Tuesday night's contests:

Trump rolls

"I consider myself the presumptive nominee," Trump said during a speech-turned-news conference in Manhattan's Trump Tower. "As far as I'm concerned, it's over."

JUST WATCHED Trump: If Clinton were a man, she would not get votes Replay More Videos ... MUST WATCH Trump: If Clinton were a man, she would not get votes 00:56

He declared Clinton easy to beat -- easier than the likes of Jeb Bush and other Republicans he's dispatched so far.

What about Cruz, his toughest primary challenger, who is vetting vice presidential candidates? "He's wasting his time," Trump said.

And that Cruz-Kasich alliance? "I think that's a good thing because it shows weakness, it shows ineffectiveness, it shows failing campaigns," he said.

Heading into Indiana , the pressure is squarely on Cruz and Kasich to prove they have a legitimate case that Trump isn't emerging as the consensus Republican choice.

On Tuesday night, Trump projected he'd win the Hoosier state, too -- underscoring a part of his appeal that no other Republicans have matched as he made his case. He pointed out that he has been criticizing Carrier, an Indianapolis-based air conditioning company that is shifting its manufacturing to Mexico, "long before I knew Indiana would be so important -- and I'm saying that won't happen if I'm President."

If the anti-Trump forces want to stop him , they'd better hope he's wrong about Indiana -- where Republican statewide candidates' internal polls show him ahead of Cruz by several percentage points. A victory there would make winning 1,237 delegates before the convention in Cleveland possible.

Clinton gets close to clinching

Big wins in Pennsylvania and Maryland have Hillary Clinton ready for a true pivot to the general election, and that means first trying to unify the Democratic Party.

As she delivered a victory speech in Philadelphia, Clinton extended an olive branch to Bernie Sanders' supporters.

"I applaud Senator Sanders and his millions of supporters for challenging us to get unaccountable money out of politics and putting greater emphasis to closing the gap of inequality," she said. "And I know together we will get that done."

She hasn't wrapped up the nomination, but her victories in Pennsylvania, Maryland and Delaware on Tuesday pushed her close enough that a loss, at this stage, would require a stunning collapse.

As Clinton loves to point out, she's much further ahead of Sanders than Barack Obama was ahead of her at this stage in 2008. Her victories in big states like New York and Pennsylvania easily erase the gains Sanders makes in smaller states.

"With your help, we are going to come back to Philadelphia for the Democratic National Convention with the most votes and the most pledged delegates," Clinton declared Tuesday night. "And we will unify our party to win this election and build an America where we can all rise together, an America where we lift each other up instead of tearing each other down."

It was the beginning of a courtship that could pick up in the days ahead. Clinton aides say the campaign will give Sanders "the space he needs" to decide his own future -- but they will be eagerly watching to see whether he dials back his critical rhetoric.

Republicans are warming to Trump

The good news for Trump went beyond the size of his victories. Exit polls showed that Republicans appear to be warming to the idea of him as the party's nominee, too.

Fewer Republican voters said they were casting protest votes. And Trump is the only candidate that a majority of Republicans in the states with exit polls -- Pennsylvania, Maryland and Connecticut -- said they'd support in the general election.

Trump won college-educated voters and white evangelicals -- two groups he hasn't consistently carried in the past.

Cruz, Kasich and the #NeverTrump movement are all angling to defeat the front-runner at the Republican National Convention in Cleveland. But in Pennsylvania, 70% of voters said they want to see the person who wins the most support in the primary as the nominee -- not, as the exit poll asked, the "best candidate."

Only 22% of Republican voters there said they'd abandon Trump in the general election -- a lower number than the two-in-five he's faced in other states.

Sanders' superdelegate pitch

Far behind in the delegate count, Sanders turned his attention to superdelegates Tuesday night, making a direct pitch to the elected officials and party power brokers who largely support Clinton to change their minds.

"What we are seeing are national polls which have us 15 or 20 points ahead of Donald Trump -- far more than Secretary Clinton," he said at a rally in Huntington, West Virginia.

JUST WATCHED Sanders: We have bigger lead over Trump than Clinton Replay More Videos ... MUST WATCH Sanders: We have bigger lead over Trump than Clinton 01:05

Sanders is still competitive with Clinton in national polls , and he has outraised the former secretary of state. But he has run out of real estate. After Clinton's romp Tuesday, it'll be all but impossible for Sanders to use the remaining contests to catch her in pledged delegates or total votes -- even if he wins California.

He sent a signal that he's accepting the harsh realities of the delegate math. In a late-night statement, Sanders said he looks forward to "issue-oriented campaigns in the 14 contests to come," adding that he will go to the Democratic National Convention "with as many delegates as possible to fight for a progressive party platform."

The biggest reason: He can't win Democrats.

Sanders draws support from independents, many of whom are new to the political process. But New York's primary last week, and most of Tuesday's contests, are closed primaries. It's no coincidence that the lone primary he won Tuesday, Rhode Island, was the only open primary.

Still, Sanders got news that will help him press forward on Wednesday: Six in 10 Democratic voters in Maryland and Connecticut see the campaign as having energized the Democratic Party rather than divided it. In Pennsylvania, two-thirds of Democrats said they'd be excited or optimistic about a Clinton presidency -- and the same share said they'd be that positive about Sanders.

Sanders' campaign may pick up with stops in Indiana's two biggest college towns -- West Lafayette, home of Purdue University, and Bloomington, the location of Indiana University -- on Wednesday. There, he'll have to articulate a case that he can still win the nomination -- a job that now appears all but impossible.

Ted Cruz is all about Indiana

Cruz knew it was going to be a bad night -- so he ignored it.

Instead, he held a rally in the historic Hoosier Gym in Knightstown, a central location from the 1986 basketball classic "Hoosiers," taking the stage 20 minutes before any polls closed, and any results were announced.

This was no election-night party. There were no televisions to display results, no open bars, no party-like atmosphere. It was billed as a campaign rally -- the same sort of event Cruz would hold any other evening.

JUST WATCHED Ted Cruz: Trump 'likely to win some states' Replay More Videos ... MUST WATCH Ted Cruz: Trump 'likely to win some states' 01:55

There was good reason for Cruz to ignore the primaries that were just wrapping up. None of the five states that voted were particularly excited about Cruz. Exit polls showed that in Pennsylvania and Connecticut, about four in 10 Republican voters say they would definitely not vote for the Texas senator if he became the GOP nominee. In Connecticut, more said they'd definitely not vote for him than definitely would vote for him. Making those numbers even more jarring: These were closed primaries. Only registered Republicans could participate.

The only mention Cruz gave Tuesday night's results came as he opened his speech -- and in the conservative crowd-pleasing form of bashing "the media's chosen candidate."

He said media executives will be the most gleeful about Trump's round of wins -- not because they support Trump, but because they see him as the weakest candidate against Clinton.

It was a way for Cruz to tee up his newest attack -- cramming "Donald and Hillary" into nearly every sentence, and laying out a list of 13 policy areas on which he said the two hold similar positions.

But conservative CNN political commentator S.E. Cupp wasn't buying it. She wrote that Cruz should stop "inventing far-fetched theories about who's really to blame for Trump's rise" because voters can see through it.

"If the media were gunning for Clinton to face the weakest Republican candidate in the field," she wrote, "they'd be gunning for Cruz, not Trump, who does even worse (and that's saying a lot) than Trump does in head-to-head matchups against Hillary."