House appropriators authored the pay-fors in their $80-billion bill to push for spending they say is needed to save teachers' jobs and pay for other issues.
President Obama has threatened to veto the House-passed measure because it makes cuts to the "Race to the Top" initiative, which rewards academically improved schools with grants, to pay for those programs.
At the end of May, the Senate passed a $58.8 billion version of the war-funding bill that has broad support of House and Senate Republicans, even though it's not paid for by cuts in spending or tax increases.
That bill has the potential to get through Congress and reach Obama's desk before the August recess.
For nearly two months, Senate Republicans have urged Democrats to find a way to pay for the six-month extension of unemployment benefits, including using stimulus money. Democrats have balked at the idea, calling the unemployment of more than 14 million Americans a legitimate emergency.
Obama made another plea to Congress on Monday to pass the bill, criticizing Republicans for holding up extension of jobless benefits.
Senate Majority Leader Harry Reid said that to many Americans "unemployment is not just a temporary inconvenience. For far too many, it's an unending emergency."
Republicans, led by Senate Minority Leader Mitch McConnell (R-Ky.) continued their argument Tuesday, saying a paid-for bill to extend benefits would've gotten bipartisan support to pass.
Republicans recalled that Obama and Senate Democrats supported a paid-for extension in November, touting that it didn't add to the deficit.
Unemployment benefits is expected to pass after the replacement for Sen. Robert Byrd (D-W.Va.) — Carte Goodwin — is sworn in Tuesday. That will give Democrats the 60 votes they need to pass the measure.One Democrat -- Sen. Ben Nelson (Neb.) has consistently voted against a measure that isn't lion in spending initiatives that aren't offset with other revenue raisers. Senators are expected to pass a $34 billion extension of unemployment benefits on Tuesday afternoon after a six-week delay caused by a Republican filibuster.