"I think there are many in the Democratic Party that want immigration to be an unsolved issue at least for the time being, because it's more useful as a campaign issue than it is as a solved issue," Rubio said in an interview with CBS News on Monday.

In June, President Obama issued a new directive that the Department of Homeland Security would stop deporting young immigrants who had been living in the country illegally for years, who would instead be allowed to receive work visas provided they meet certain criteria.

After Obama made the announcement, Rubio, who's said to be a top candidate for the vice presidential spot on the 2012 Republican ticket, announced that he would not be unveiling a Republican alternative to Democrat-backed Development, Relief, and Education for Alien Minors (DREAM) Act, immigration reform legislation meant to protect young immigrants who came to the country illegally from being deported — similar to Obama's policy directive. Rubio had previously been planning to put his proposal in bill-form sometime in the summer.

Both Obama's policy directive and Rubio's alternative immigration reform proposal, unlike the DREAM Act, do not provide a pathway to citizenship for the targeted young immigrants.

Despite expressed willingness by both Republicans and Democrats to work with the opposing party to craft comprehensive immigration reform, Congress has remained unable to pass legislation.

Rubio said the only way to institute substantial immigration reform is for Democrats to stop using it as a political weapon against Republicans.

"I think it starts with making a commitment to not continue to use it as a political tool. I mean the president can give whatever speech he wants but the truth is that he and his party continuously use immigration as a bat to beat Republicans over the head with," Rubio added. 

Democrats have repeatedly responded to similar criticism noting that Republicans blocked the DREAM Act from passing the Senate. 

"Sen. Rubio has some serious amnesia about his party's long obstruction record on immigration reform and an even worse inflammatory rhetoric. For a recent example he should refer to Speaker BoehnerJohn Andrew BoehnerDems face hard choice for State of the Union response Even some conservatives seem open to return to earmarks Overnight Finance: Trump, lawmakers take key step to immigration deal | Trump urges Congress to bring back earmarks | Tax law poised to create windfall for states | Trump to attend Davos | Dimon walks back bitcoin criticism MORE, who all but shot down his idea in the House," a Democratic Senate aide said. "Rubio should be praising the President for doing something concrete to help these young people and joining Democrats to craft a permanent solution."

—This story was updated Tuesday at 1:55 p.m.