Richard Durbin, a Democratic senator, said his party was open to Republican amendments to the stimulus package.
"We've said to them, 'We're open about this. Come to us with your ideas, if you want to make changes and offer amendments,'" he said on Fox News Sunday.
McConnell has put forward a plan to provide government-backed, four per cent fixed mortgages to credit-worthy home buyers, saying it could save them an average of $5,600 a year.
Obama also programmed a fresh round of talks with congressional leaders on Monday to try and avoid deadlock over the measures.
"The thing I want all of them [congressmen] to remember, and the thing I am thinking of every single day, is the thousandsof people being laid off from their jobs right now," Obama said in an interview with the NBC television network.
"They can't afford politics as usual and old habits are hard to break, but now is the time to break them because we have an urgent situation."
Democrats hold a majority in the senate, but do not have the 60 seats needed in the to overcome a "filibuster", a parliamentary move that would stop the plan from going to a vote.
"A super-majority is required for virtually everything in the Senate, and certainly for something that is close to a one trillion dollar spending bill, it will," McConnell said.
Every Republican legislator voted against the bill in the House of Representatives, amid concerns that the package included too little in tax cuts and too much in spending.
They said the plan would burden the government with new budget obligations.
Democrats have, so far, rejected all efforts to shift the package away from infrastuctural and social spending, and towards new tax cuts.
In the last three months of 2008 the national economy declined 3.8 per cent, marking its worst contraction in 25 years. The rate could accelerate to five per cent in 2009.