Rubio slams latest Obama jobs proposal

"I support a real jobs plan. I don't think what we voted on today is a real jobs plan. I think it's another bailout of local governments," said Rubio in a Web video posted Thursday.

The $35 billion Democratic measure was designed to prevent layoffs of teachers, police officers and firefighters in cash-strapped states. Most of the funding, $30 billion, would have gone to saving teaching jobs, with the rest of the money directed to first-responders.

Rubio made the issue personal in his video statement, saying although he has firefighters and teachers in his own family, he could not support more spending when there is already massive federal debt.

"We can not afford to be bailing out local governments. We can not afford stimulus 2.0. We can not afford another stimulus program, which is what the president is proposing," he added.

For the second time in two weeks, Senate Republicans voted in unison to block "jobs" legislation, which the Obama administration and Senate Democratic leaders have made central to their agenda.

The majority of Democrats then blocked a second "jobs" measure offered by Republicans that would have eliminated a rule requiring the federal government to withhold a 3 percent tax from federal contracts.

The Florida senator called for Republicans and Democrats to come together and pass the parts of the two proposed jobs bills that overlap.

For more on Thursday's proposed legislation from both sides of the aisle, click here. 

—Alexander Bolton and Josiah Ryan contributed.