TALLAHASSEE -- As his popularity appears to plummet, Miami-Dade Mayor Carlos Alvarez could face a challenge from Florida House Speaker Marco Rubio, who's not ruling out a run for mayor and whose poll numbers suggest he would be a strong candidate.

''I haven't made any decisions about anything,'' Rubio said Friday when asked if he would challenge Alvarez. ``I'm just so focused on being speaker. To start answering questions like that invites lots of other questions.''

But Rubio acknowledges he has been asked to run by supporters, who have been bolstered by a new survey from Florida International University's polling institute suggesting Alvarez is at his politically weakest point.

About 41 percent of respondents said they disapproved of Alvarez's job performance, compared to 38 percent who approved, according to the poll of 842 west and central county residents in commission districts 9, 10, 11 and 12.

Those numbers are a steep drop from 2006, when Alvarez's approval ratings were at 70 percentage points, said FIU pollster Dario Moreno. Meantime, he said, Rubio's approval numbers have climbed since 2006.

The reason the two have passed each other: Property taxes and government spending, Moreno said.

Rubio made himself the face of deep tax cuts that, though they estranged politicians in county hall and the Capitol, made him more popular in Miami-Dade. Alvarez, meanwhile, said little of the issue before the Jan. 29 vote and has pushed for a massive $3 billion ''Global Agreement'' spending plan on a baseball stadium, a port tunnel, a ''museum park,'' and other projects.

''People are wondering why there's all this money to pay for this stuff but not enough money to pay for healthcare or tax cuts,'' Moreno said.

In a Sunday op-ed column in The Miami Herald, Rubio seized on the ''shell game'' of a plan as a reason to advocate for more spending caps.

Alvarez hit back at the speaker in a Friday letter that said those who ``float innovative ideas and talk about public policy in the abstract are just delivering empty rhetoric.''

Said Alvarez spokeswoman Victoria Mallette: ``While he does not govern by polls, he realizes there is rarely universal support for any issue.''

Moreno and political insiders say a Rubio-Alvarez match-up would be a battle royale, because both men share support from the same base: West Dade Hispanic Republicans.

Moreno said that in the last poll he took of the two politicians, before the Jan. 29 election, both had 40 percent approval ratings, though 25 percent disapproved of Rubio and 34 percent disapproved of Alvarez.

So far, Alvarez's only declared challenger in the August election is Helen Williams, a former Miami-Dade teacher who often speaks at School Board meetings.

Miami Republican Sen. Alex Villalobos ventured this about a Rubio run: ``I hope he tries. Carlos Alvarez will clean his clock. He's still popular. He's effective.''

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