* McMorris Rodgers attacks Obamacare
* Senators Paul and Lee also vie for Republican spotlight
By Richard Cowan and Thomas Ferraro
WASHINGTON, Jan 28 (Reuters) - Republicans in the U.S. Congress responded in competing voices on Tuesday to President Barack Obama's annual State of the Union address as various wings of the party vied to advance their prescriptions for the country's best way forward.
Representative Cathy McMorris Rodgers, who delivered the sanctioned Republican response to Obama, queued up long-standing party doctrine that "champions free markets and trusts people to make their own decisions, not a government that decides for you."
McMorris Rodgers, a five-term congresswoman from Washington state, took a broad swipe at Obamacare, the 2010 landmark healthcare law that Republicans have tried to repeal, delay or significantly alter nearly 50 times since its enactment.
"We've all talked to too many people who have received cancellation notices they didn't expect or who can no longer see the doctors they always have," McMorris Rodgers said of the Affordable Care Act, which got off to a troubled start.
"No, we shouldn't go back to the way things were, but the president's health care law is not working," she said.
Republican Senators Rand Paul of Kentucky and Mike Lee of Utah, two favorites of the anti-Washington Tea Party movement, staged separate responses to Obama's speech.
Paul, who joined the Senate in 2011 and is often mentioned as a possible 2016 presidential candidate, appealed to the conservative base of the Republican Party.
"Economic growth will come when we lower taxes for everyone," Paul said. "Government spending doesn't work."
McMorris Rodgers is relatively unknown nationally, even though as No. 4 House Republican she is the highest-ranking female member of her party in Congress. She also holds the distinction of being the only person to give birth three times while serving as a member of the House of Representatives.
Discussing her eldest child's Down syndrome diagnosis, McMorris Rodgers brought a softer tone to her party, which is often accused by Democrats of helping the rich at the expense of the poor and middle-class.
"Today, we see a 6-year-old boy who dances to Bruce Springsteen, who reads above grade level and who is the best big brother in the world," McMorris Rodgers said, adding, "We see all the things he can do, not those he can't."
Her moment in the limelight came as Republicans see November's congressional elections and the 2016 race for the White House as opportunities to close a "gender gap" that contributed to their 2012 election losses.
That gender gap was on full display in 2012, when Obama received 55 percent of women's votes, while failed Republican presidential candidate Mitt Romney got 44 percent.
Even as Republicans tried to broaden their appeal with women voters, they pushed through the House on Tuesday a partisan bill that would make it more difficult for some women to get abortions.
One year ago, a USA Today/Gallup poll found that by a 53-percent-to-29 percent margin, Americans said they wanted the Roe v. Wade Supreme Court decision granting abortion rights to be kept in place.
A SECOND GAP
Attacking another gap - among Hispanic-American voters - Republican Representative Ileana Ros-Lehtinen of Florida delivered a speech closely tracking McMorris Rodgers' but spoken in Spanish.
In 2012, Obama won 71 percent of the Hispanic vote to Romney's 27 percent. Since then, House Republicans have blocked comprehensive immigration reform moves that are important to Latino voters.
In his address to a joint session of Congress, Obama called for finishing work this year on comprehensive immigration reform.
Ros-Lehtinen was vague about immigration reform's prospects in the House, noting that Congress needed to "fix our broken immigration system with a permanent solution," she said in a Reuters translation of her remarks.
On Thursday, House Republican leaders are expected to make public their "principles" for pursuing immigration reform this year. It was unclear whether those principles will advance any further amid deep Republican divisions.
An outspoken opponent of such legislation, Representative Lamar Smith of Texas, on Tuesday warned: "Ten million Americans are unemployed and millions more have given up looking.
"We should put them first," before giving "work permits" to people who came to the United States illegally, Smith said.
Like McMorris Rodgers, Senator Lee also demanded a smaller federal government.
The rise of the Tea Party helped Republicans win control of the House in the 2010 elections, but some of its Senate candidates in the past few elections have fallen short, leaving that chamber in the hands of Democrats.
Nevertheless, the Tea Party's war against large federal budget deficits set the agenda for Congress in 2011, 2012 and 2013, when Democrats and Republicans battled each other over spending cuts.
Tea Party initiatives, Lee said, ranging from welfare and criminal justice reforms to ending corporate subsidies, "will put Americans back to work, not just by cutting big government, but by fixing broken government."
After all the pomp of a presidential State of the Union speech, complete with standing ovations and celebrities in the audience, McMorris Rodgers, Lee and Paul may have known they would have a tough act to follow with their response speeches.
"Someday, the party not in the White House is going to figure out that these are not a good idea. The optics are always terrible," said Paul Sracic, head of Youngstown State University's political science department in Ohio.
"How can you not look small when compared to a president addressing both houses of Congress," Sracic said.