(corrects paragraph 4 to say letter went to Steny Hoyer)

By Steve Holland

WASHINGTON, July 10 (Reuters) - President Barack Obama's core legislative agenda -- overhauling healthcare and addressing climate change -- has hit some stumbling blocks in the U.S. Congress.

Here are some questions and answers about the issues.

WHAT'S GOING ON WITH THE HEALTHCARE OVERHAUL?

Dozens of fiscally conservative Democrats, worried about the estimated $1 trillion cost, are demanding some big changes in a healthcare plan working its way through the House of Representatives. That likely will delay the official roll-out of a version of the legislation on Friday.

In a Thursday night letter to Democratic House Speaker Nancy Pelosi and No. 2 House Democrat Steny Hoyer, about 50 House Democrats said the House should "pare back some of the cost-drivers to produce a bill that we can afford."

Healthcare is Obama's top legislative priority and he wants to sign a bill by the end of October to make healthcare more affordable for millions of Americans who are either having trouble paying for health insurance or doing without.

But the cost of the program -- and how to pay for it -- may force Obama to forswear his campaign pledge not to raise taxes on anyone making less than $250,000 a year.