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By Kevin Drawbaugh and Patrick Rucker

WASHINGTON, April 1 (Reuters) - Democrats and Republicans in the U.S. Senate agreed on Tuesday to draft a housing rescue bill that could deliver billions of dollars to homeowners facing foreclosure and help steer the economy away from a deep recession.

Democratic leaders want the federal government to pay for more mortgage counselors, rehab projects for empty homes and tax breaks for borrowers stuck in unaffordable loans. Perhaps the most controversial provision of their plan would let bankruptcy judges erase some mortgage debt.

Lawmakers and policy-makers on all sides agree that the country is facing a tough economic crisis led by a wave of failing home loans, but Republicans generally resist a big government bailout.

Earlier this year, Democratic lawmakers failed to muster enough votes to carry their agenda unilaterally and so decided to work with Republicans.

Setting a deadline of noon on Wednesday to reach a bipartisan deal, the senators said they would try to overcome deep disagreements over the scope of the legislation.

"Bipartisan senators are committed to moving forward with legislation," Senate Majority Leader Harry Reid, a Nevada Democrat, told reporters.

Senate Minority Leader Mitch McConnell, a Republican from Kentucky, said senior members of the Senate Banking Committee would work together over the next 24 hours to merge proposals from both parties.