Steny Hoyer, a Maryland Democrat who is House Majority Leader, said earlier hopes that a package could be ready for incoming President Barack Obama to sign into law on his January 20 inauguration were excessively optimistic.

"We certainly want to see this package passed through the House of Representatives no later than the end of this month, (and then) get it over to the Senate and have it to" Obama to sign by the middle of next month, Hoyer told "Fox News Sunday."

Senate Majority Leader Harry Reid, a Nevada Democrat, said any stimulus package must have bipartisan support. He said Congress will move as quickly as possible but declined to predict when it will have one ready for Obama to sign.

Asked if the pricetag could hit $1 trillion, Reid said; "It's whatever it takes to bring this country back on a fiscal footing that is decent. We don't want to do a little bit and say, 'Well we should have done more.'"

"We want to do it right the first time," Reid told NBC's "Meet the Press."

Senate Republican Leader Mitch McConnell voiced concerns about how quickly Democrats may push a package of middle class tax cuts and new spending and what may be included in it.

But McConnell said Obama could ultimately win broad Republican support if Republicans are given a fair opportunity to shape it.

"I think if they pursue a fair process, in the Senate at least, where fairness is typically the rule, and give both sides an opportunity to have input, to have it -- a true bipartisan stamp -- he's likely to get significant support," McConnell told ABC's "This Week."

(Reporting by Alan Elsner, Will Dunham and Thomas Ferraro editing by Sandra Maler and Philip Barbara)