* Trump set to meet with Democratic senators on taxes
* White House, Republican lawmakers have not devised tax plan (Adds background on budget resolution, Representative Black comment)
WASHINGTON, Sept 12 (Reuters) - U.S. Treasury Secretary Steven Mnuchin cast doubt on Tuesday on President Donald Trump's goal of cutting the corporate tax rate to 15 percent, even as the president moved to inject new urgency into a sluggish effort in Congress to lower taxes.
"Ideally, he'd like to get it down to 15 percent. I don't know if we'll be able to achieve that given the budget issues, but we're going to get this down to a very competitive level," Mnuchin told a conference in New York hosted by CNBC.
The administration is cranking up a publicity campaign to build public support for the Republican president's tax goals. Trump was set to dine at the White House with six senators - including three Democrats - later on Tuesday to discuss taxes.
But neither the administration nor the Republicans who control Congress have agreed on a detailed plan for overhauling the tax code, which was one of Trump's main campaign promises in 2016, despite months of discussions.
A major concern is not adding to the federal budget deficit. It would balloon if tax rates were cut too deeply without providing offsetting federal spending reductions and closure of tax loopholes, both politically difficult tasks.
Mnuchin declined to say what business tax rate was achievable. He said he was "incredibly hopeful" a tax plan could be enacted this year, adding it could be retroactive to January.
Asked whether Trump would hold out for a 15 percent corporate tax rate, compared with the current 35 percent, White House spokeswoman Sarah Sanders said: "The president is prepared to push for as low of a rate as we can get. We're going to continue to push for that and work for Congress to make sure we get the best deal possible."
Republican Paul Ryan, the Republican speaker of the House of Representatives, said last week that "the numbers are hard" to make Trump's 15 percent corporate tax rate target work. Ryan set his own goal at around 22.5 percent.
Trump's legislative affairs director, Marc Short, said at a Christian Science Monitor event that "there's probably compromise" necessary to get a deal, but "we think that what's best for the American people is a 15 percent corporate rate right now."
'NO NEW DEBT'
Senator Joe Manchin of West Virginia, one of the three Democrats due to dine with Trump on Tuesday, said he was prepared to work with the president on taxes so long as it did not add new debt to the national balance sheet.
"No new debt, anything that shows me it's going to add debt to our nation. I've got 10 grandchildren. I'm not going to do that to them," Manchin said.
Financial markets rallied after Trump's election victory last November in anticipation of rapid tax cuts, especially for corporations, but those expectations have faded.
"The likelihood of passing sweeping corporate reform has diminished," Jack Ablin, chief investment officer at BMO Wealth Management, said in a research note.
Republican lawmakers have said that Trump's legislative deal with Democrats last week to help hurricane victims and keep the government running for three more months could complicate the tax effort.
Democrats, who generally oppose tax cuts for the wealthiest Americans, will have negotiating clout in Congress in early December to resist tax changes they oppose, also potentially including a corporate rate cut.
Trump may visit as many as 13 states to sell his planned tax cuts to voters in coming weeks, the White House said.
The White House said the senators who would dine with Trump were Democrats Manchin, Joe Donnelly and Heidi Heitkamp, along with Senate Finance Committee Chairman Orrin Hatch and fellow panel Republicans Patrick Toomey and John Thune.
The U.S. Senate will begin tax overhaul hearings this week, with an important procedural hurdle looming ahead.
Republicans have firm control of the House, but only a 52-48 Senate majority. Both chambers must approve a 2018 budget resolution to unlock a legislative tool called reconciliation that would let Republicans pass a tax bill by a 51-vote majority in the Senate, rather than the standard 60-vote margin that requires support from at least some Democrats.
The House Budget Committee approved a budget resolution in mid-July that would combine tax cuts with spending cuts to programs such as food assistance for the poor.
The measure has stalled in the House amid party infighting over the spending cuts. Some Republicans also want to see a clearer tax plan before committing to the budget measure.
House Budget Committee Chairman Diane Black told Reuters she hoped for a House vote on the measure at the end of the month.
Republican Senator John Kennedy, a budget committee member, told Reuters he wanted tax plans "with specificity" and expressed frustration at the slow pace of the tax debate.
"No more platitudes. Let's see some meat on the bone," Kennedy said. "You don't always get what you want. I think there's a song that says that. But you need to get what you need and that's where we are. And I'm tired of screwing around. ... The American people are tired of screwing around."
(Additional reporting by Roberta Rampton in Washington; Brendan O'Brien in Milwaukee; Dan Burns in New York; and Svea Herbst in Boston.; Writing by Alistair Bell; Editing by Kevin Drawbaugh and Peter Cooney)