Schumer said that Democrats would "unite" to block any effort to link the two.
Supporters of the program are banking Tea Party critics won’t risk a shutdown.
The bill passed 319-108, one year after a fight between the GOP and Obama led to a shutdown.
Rank-and-file Dems and Republicans have expressed concerns over the Syria measure.
Boehner says a vote will come next week as GOP grapples with Obama's Syria request.
“I know he does,” Pelosi said. “I've studied this issue for a really long time."
Republican leaders plan to hold a vote on the measure Thursday in the House.
“The only people talking about a government shutdown are the Democrats," he said.
Pelosi said the issue was one of "economic patriotism."
The Senate voted 86-14 for a bill that keeps the government funded through Saturday.
The continuing resolution would keep the government running through Saturday.
House Majority Leader Eric Cantor (R-Va.) said he expects the House to pass a short-term continuing...
“The fight is now, not next year,” said Mike Needham, Heritage Action’s CEO.
The bill will prevent a government shutdown on Oct. 1.
The group said the ISIS language made the vote "driven by foreign policy."
The House released a Syria measure Monday, likely clearing the way for votes.
Boehner did not say if a plan to arm Syrian rebels would be attached to a funding measure.
Lawmakers put off a vote after Obama asked for authority to equip Syrian rebels.
The bank may only be safe until June, leaving both sides disappointed.
"I'm interested to see what kind of ideas my colleagues have," he said.
The House may vote on a continuing resolution before the August recess.
The House will meet in the afternoon to take up a $1 trillion spending bill that's more than 1,500...
Lawmakers approved a bill funding the government through Saturday.
Currently, the House has nine legislative days in September to tackle Syria, immigration, the debt...