"We can be working simultaneously," she told the Sun-Times, which reported her comments late Monday.

Pelosi said she wants a bipartisan bill because that's the only way to get the needed 218 votes for House passage. But last week, Speaker John BoehnerJohn Andrew BoehnerRestoring fiscal sanity requires bipartisan courage GOP congressman slams primary rival for Ryan donations Speculation swirls about Kevin McCarthy’s future MORE (R-Ohio) indicated that House Republicans would not be rushed by Senate passage of an immigration bill, which could happen by June.

"We're not going to be stampeded by the White House or stampeded by the president," he said. "The Senate is working its will. A lot of good work that's gone on over there. But the House is going to work its will."

In the House, a bipartisan group of members got closer to a deal last week, but were still hung up on the issue of whether and how illegal immigrants should have healthcare coverage if they are moving toward U.S. citizenship.

Earlier in May, the Senate Judiciary Committee approved an immigration bill that would create a path to citizenship for 11 million illegal immigrants. Many House Republicans have criticized that bill as one that only promises more border enforcement, a sign that a House GOP bill will include more strict border enforcement measures.