(CNN) - Democratic Sen. Chuck Schumer, part of the bipartisan "Gang of Eight" on immigration reform, predicted Sunday that the Senate will pass his group's bill by July 4.
"We're going to put immigration on the floor by June 10. I predict it will pass by July 4," he said. "We're hoping to get up to 70 votes."
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But is Schumer engaged in wishful thinking?
His comments came just days after a new Quinnipiac University poll indicated more than two-thirds - 71% - of Americans doubt Congress can work together to move forward on immigration reform. Schumer's optimism also came just over a week after his fellow Gang of Eight member, Democratic Sen. Bob Menendez, warned that the group didn't yet have the 60 votes needed to overcome a filibuster in the Senate.
Schumer also vowed the string of recent controversies hitting the Obama administration will not be a distraction.
"We are moving forward because we believe in a bipartisan way this is so vital for America. We'll have a good bill," the senator from New York said on NBC's "Meet the Press."
And despite warnings from the GOP-controlled House of Representatives that the Senate bill will fail to gain traction, Schumer argued House Speaker John Boehner will have no choice.
"Congressman Boehner is in a box. There are about 60 or 70 of his people who are against any immigration reform," Schumer said. "But at the same time, he knows that the Republican Party will be consigned to a minority party for a generation if they're anti-immigration."
If the Senate can gather a majority of Republican senators and almost every Democrat, then "that may change the equation in the House and the thinking in the House among mainstream Republicans," Schumer said. "They may want to go for our bill."
Not so fast, said Republican Rep. Ileana Ros-Lehtinen.
The congresswoman from Florida said Sunday the "Senate bill is not going to move in the House."
"I think the speaker has made it clear that we will have our own work product," she said on CNN's "State of the Union."
While a bipartisan group has been working on an immigration plan in the House and says it has reached a deal, the group has yet to formally introduce its legislation.
Boehner has applauded that group's efforts and said in a joint statement with the other three top House Republican leaders that the House will take its own path on immigration.
"The House remains committed to fixing our broken immigration system, but we will not simply take up and accept the bill that is emerging in the Senate if it passes. Rather, through regular order, the House will work its will and produce its own legislation," the GOP leaders said.
Ros-Lehtinen said Boehner favors a "piecemeal approach" rather than a comprehensive package like the Senate bill.
"I don't know if we'll have comprehensive reform or we will have it piece by piece, but that Senate bill may not even pass the Senate itself," she added.
Rep. Bob Goodlatte, R-Virginia, further backed the step-by-step approach and argued on "Fox News Sunday" that any bill passed should not include a pathway to citizenship - something that's included in the Senate bill.
As for legal status, Goodlatte takes the position of many Republicans, stating that the government must enforce several other border security and interior measures first.
On the same Fox program, Rep. Chris Van Hollen, D-Maryland, said Congress should be able to tackle multiple issues at a time, including immigration in addition to the recent controversies surrounding the IRS and the Justice Department.
"We should be able to walk and chew gum at the same time," he said.
- CNN Senior Congressional Producer Deirdre Walsh contributed to this report.