(CNN) -- President Barack Obama urged Congress on Monday to pass an extension of unemployment benefits, saying that Senate Republicans have allowed short-term political concerns to trump the needs of the jobless.

During an appearance in the Rose Garden, Obama argued that that the federal government has "a responsibility to offer emergency assistance to people who desperately need it" and an obligation to help families "make ends meet."

The Senate is set to consider a bill Tuesday that would extend the deadline to file for unemployment benefits through the end of November. The bill would cost $33 billion in additional deficit spending, according to the Congressional Budget Office.

Senate GOP leaders have blocked a vote several times, highlighting deficit concerns by arguing that any benefits extension should be offset by spending cuts. Democrats are counting on the seating of the replacement for Sen. Robert C. Byrd of West Virginia on Tuesday to break the logjam.

In his remarks at the White House, Obama said that three times in recent weeks, a "partisan minority" has used "parliamentary maneuvers" to block a vote on extending unemployment benefits. The Republicans are guided by a "misguided notion" that a new relief bill would discourage people from looking for work, he said.

"That attitude reflects a lack of faith in the American people," Obama said. People "aren't looking for a handout. They desperately want to work."

The Republicans should stop holding people "hostage to Washington politics," he declared. "There are times when you put elections aside. This is one of those times."

House Minority Leader John Boehner, R-Ohio, immediately fired back, releasing a statement slamming Obama for fiscal irresponsibility.

"The president knows that Republicans support extending unemployment insurance, and doing it in a fiscally responsible way by cutting spending elsewhere in the $3 trillion federal budget. At a time of record debt and deficits made worse by Washington Democrats' massive spending spree, that's the right thing to do and the right way to do it. The American people are asking 'where are the jobs?' and President Obama continues to offer only disingenuous attacks, not answers."

More than a million Americans are estimated to have exhausted the unemployment benefits lifeline since the deadline expired in June.

The U.S. unemployment rate stood at 9.5 percent as of June. The jobless rate has averaged 9.7 percent over the first half of the year, and many economists expect it to remain elevated into 2011.

Before last month, out-of-work Americans were eligible for extensions once they maxed out at 26 weeks of state benefits.

Depending on the state, people could qualify for up to 73 weeks of federal benefits -- a total of 99 weeks. But, citing deficit concerns, Senate Republicans blocked the extension with a 57-14 vote before the July Fourth holiday.

Seventy-eight percent of Americans still believe the U.S. economy is in a recession, according to a CNN/Opinion Research Corp. poll released last month. Forty-one percent believe Republicans are more responsible for the nation's current economic problems, while 28 percent blame the Democrats. Twenty-six percent blame both political parties.

CNN's Dan Lothian, Alan Silverleib and Aaron Smith contributed to this report