Dodd, D-Conn., also said Congress needs to help homeowners in distress. He has called for lenders to offer new, more affordable mortgages in exchange for greater financial backing by the Federal House Administration, which pays a claim to the lender in the event of a homeowner's default.
"The heart of this economic problem is the foreclosure problem," Dodd said.
Sen. John Cornyn, R-Texas, did not rule out a second aid plan, but is worried about the potential costs.
It is too early to gauge the economic impact of the $168 billion measure passed by Congress and signed by President Bush in January. Rebate checks of up to $1,200 per couple and even more for families with dependent children will start arriving in mailboxes in May.
Bush has argued against additional relief plans at this time.
"Everything I hear coming from my friends on the other side of the aisle is, `Let's have the federal government spend more money,"' Cornyn said. "And that money comes from your pocket and mine. And I think we ought to be careful.
The second-ranking Democratic senator, Dick Durbin of Illinois, said he wants to extend unemployment benefits. He said the war is adding about $12 billion to $15 billion to the deficit each month.
"But when we suggest putting money in this economy to help struggling families, unemployed families and those who are trying to get by, the Republicans quickly say, `Oh, this is a big deficit problem."'
Durbin was not the only Democrat who referenced the war when talking about the economy. Rep. John Murtha, a leading critic of the war, said the United States was spending too much money in Iraq.
"When I'm home, you know what I hear? I hear, what about our roofs; what about our sewage and water; what about the things that need to be done in the United States?" said Murtha, D-Pa.
The lawmakers appeared on "Late Edition" on CNN.