The debate produced few fireworks as the candidates stuck to well-worn themes that have been featured in a barrage of television ads.
Murray, who is seeking a fourth term, continually hammered Rossi for supporting extension of the Bush-era tax cuts that benefit the wealthy. She said those tax breaks take away revenue that could be used for Social Security, Medicare and health programs.
"If Mr. Rossi gets his way and extends the Bush tax cuts to the wealthiest Americans to the tune of almost $1 trillion, there is no way to sustain the programs so important to us," Murray said. "You can count on me to make sure our parents are taken care of."
Rossi criticized Murray as a three-term incumbent who constantly voted for bigger government programs and more government control of business.
"You have an 18-year incumbent killing jobs in the state of Washington in vote after vote after vote," Rossi said. "I want to allow entrepreneurs to be successful."
Although polls have been inconclusive, the race is thought to be close as Democrats try to hold control of the Senate.
The hourlong debate was held in the studios of public television station KSPS. The candidates' second and last scheduled debate is Sunday in Seattle, hosted by KOMO-TV.
Before the debate, a man drove past the studio building several times brandishing a meat cleaver out the window of his vehicle at Murray supporters. He was arrested by Spokane police.
As she has done throughout the campaign, Murray painted Rossi as a friend to Wall Street and big banks. Rossi, a real estate developer who has twice lost races for governor, branded Murray as a big-spending liberal.
They referred constantly to the fight over extending the 2001 and 2003 tax cuts to individuals making more than $200,000, bringing it up in the context of numerous issues.
Rossi said the country was heading in the wrong direction because of uncontrolled spending such as the health care reform bill. Murray said families are struggling because of the greed of Wall Street.
Murray said the country needed targeted investments in places like education to create more jobs. Rossi contended lower taxes and predictable costs for items like health care will allow businesses to create jobs.
"We are going to have the biggest tax increase in American history" if the Bush tax cuts are not extended, Rossi said.
Both candidates supported continued cleanup of nuclear waste at Hanford, but Murray said the government needs the money to do that.
Rossi attacked the health care reform bill, saying it would dramatically increase costs for key employers like Boeing. "This eventually could bankrupt America," Rossi said.
"The only people that health care was working for was health insurance companies," Murray responded.
Murray said she supported getting banks out of the business of giving student loans, so that money was funneled to students and not into profits for the banks.
"Part of the takeover by government is student loans," Rossi responded, saying having banks administer loans provided students more options.
Asked to say something they admired about their opponent, Murray said she admired Rossi for making the sacrifices to get into the race. Rossi said he believed Murray had done good work for veterans.
But he said she was part of the partisan fighting in Washington, D.C., that has turned off many Americans.
"We have a serious problem here with a very partisan U.S. senator," Rossi said.
Murray said voters have a clear choice in this election.
"He wants the Bush economic policies that got us into this mess," she said.
Rossi, 50, lost to Democratic Gov. Chris Gregoire by 133 votes in 2004 after two recounts. He lost to her by nearly 200,000 votes in 2008. He is seeking to capitalize on anti-incumbent sentiment in a state that has voted Democrat the past six presidential elections.