Sen. Marco Rubio, R-Fla. listens at left as Republican presidential candidate, former Massachusetts Gov. Mitt Romney speaks during a news conference prior to a town hall-style meeting in Aston, Pa.
(CBS News) -- President Obama's decision to make it easier for hundreds of thousands of illegal immigrants to stay in the United States makes it more likely rival Mitt Romney may pick Florida Sen. Marco Rubio to be his running mate, CBS News chief Washington correspondent Bob Schieffer said Monday.
"I think it puts Rubio on the short list. I don't think there is any question about that," Schieffer said in an interview with "CBS This Morning" two days after interviewing the former Massachusetts governor for CBS' "Face the Nation."
Mr. Obama announced last week that the government would not deport immigrants who can prove they were brought to the United States before they turned 16 and are younger than 30, have been in the country for at least five continuous years, have no criminal history, graduated from a U.S. high school or earned an equivalent diploma or certificate, or served in the military.
Schieffer said that Romney's non-answers on whether he supports Mr. Obama's decision suggests the presumptive Republican nominee still has not yet made up his mind on the matter.
"I think they are still crafting what Gov. Romney's position on this would be," Schieffer said, noting that Romney "cannot be unaware of the growing power of the Hispanic vote."
Rubio is Cuban American and Cuban Americans in the key battleground state of Florida traditionally voted Republican but "now you have a number of non-Cuban Hispanics in Florida ... and they do not, the non-Cuban Hispanics do not always tend to vote Republican. A lot of them are Democrats."
Schieffer noted that Romney is holding his cards close to the vest on what will be the biggest decision of his campaign.
While Rubio is certainly under consideration, Schieffer told host Charlie Rose "if there's one thing I came away from all of this with is Gov. Romney has not made up his mind who his vice presidential running mate is going to be."
"He may know in his heart of hearts, but he's not making any -- getting any hint of who it's going to be. In fact, one of the reasons I didn't even ask him during the interview is because before the interview and all week I've been talking to people on the campaign. They said, look -- he's not going to tell you. You can ask him, but you're not going to get any news on that. So I didn't bring it up," he said.