The next U.S. presidential primary contest is more than a week away, but there is no lull in campaigning as front-runners in both parties look to boost their delegate leads and challengers argue the nomination could still fall within their grasps.

The all-critical delegate math is far more straightforward on the Democratic side than on the Republican.

Republican Ted Cruz and Democrat Bernie Sanders won big last week in Wisconsin but face tough odds next week in New York, Donald Trump’s home state.

“It is great to be home. This is home,” Trump said about New York.

Republican presidential candidate Donald Trump spe
Republican presidential candidate Donald Trump speaks during a rally at JetSmart Aviation Services, in Rochester, N.Y., April 10, 2016.

New York also is the state Hillary Clinton once represented as a senator.

“Whoa, hello, Sunset Park! Hello, Brooklyn!” she said.

With time dwindling to overtake the front-runners in the delegate count, challengers are waging battles of perception.

Sanders insists he retains a path to the nomination.

Democratic presidential candidate, Sen. Bernie San
Democratic presidential candidate, Sen. Bernie Sanders, I-Vt., orders hot dogs at Nathans Famous in Coney Island in the Brooklyn borough of New York, Sunday, April 10, 2016.

US Presidential Candidate Delegate Count

“If we can win here, it absolutely opens the door to a path toward victory to the White House," said Sanders. "When the voter turnout is high, we win.”

Cruz, meanwhile, is making a more complicated argument: that he could win the nomination even if he trails Trump in delegates heading into the Republican National Convention in July.

“If we go into a contested convention, we are going to have a ton of delegates," Cruz said. "Donald [Trump] is going to have a ton of delegates. We will go in with an overwhelming advantage. I believe the first ballot will be the highest vote total Donald Trump receives. And on a subsequent ballot, we are going to win the nomination.”

After a poor showing in Wisconsin, Trump shook up his campaign staff. But his rhetoric is unchanged.

“Lying Ted Cruz came today," Trump said. "He could not draw 100 people. A hundred people.”

Clinton, meanwhile, said she is impatient to wrap up the Democratic contest so she can focus on the general election.

Democratic presidential candidate Hillary Clinton
Democratic presidential candidate Hillary Clinton exits after speaking at New Greater Bethel Ministries during a campaign stop,in New York, April 10, 2016.

“We are on the path to the nomination, but I need to win big here in New York, because the sooner I can become the nominee, the sooner I can turn and unify the party – and the sooner we can go after the Republicans fulltime,” Clinton said.

Polls show Clinton and Trump with substantial leads in New York.