President Reagan, in what aides agreed was a sign of growing Republican nervousness over the pre-election unemployment rate, yesterday threw his weight behind a compromise job training bill that had been bogged down in a House-Senate conference for more than a month.

He urged swift enactment by Congress, calling the bill "a hand up, rather than a handout" for the disadvantaged.

The White House had threatened a veto of the bill in some of its earlier forms. Senate Labor Committee Chairman Orrin G. Hatch (R-Utah) said the bill now could be moved quickly to passage, perhaps before Congress goes home for its election recess early next month.

"The bottom line is how the hell do you veto a jobs bill when the unemployment rate is approaching 10 percent," an administration official said of the president's new enthusiasm for the training legislation.

A re-tooled, scaled-down version of the controversial Comprehensive Education and Training Act (CETA) program, the training bill would funnel 70 percent of all funds for training, as opposed to payments to participants and administrative costs.

The funds are expected to be somewhere between $3.8 billion and $5.4 billion a year. The bill would help more than 1 million poor and jobless people yearly, officials said.

Unlike CETA, which expires Thursday, this bill would not pay for what Reagan called "make-work" public-service jobs, which inspired scandal and made CETA unpopular.

The bill would prohibit the use of funds to pay participants stipends while they take the training, a point insisted on by the Republican-controlled Senate but opposed by the House, which wanted to allow such support. Opponents of the stipends argued that many young participants would take the money and ignore the training.

The unemployment rate is 9.8 percent. The Democrats have been flogging Republicans with the issue. The polls show it as a prime concern of likely voters. And there is one more report on unemployment due out, on Oct. 8, before the Nov. 2 elections. Many economists think that report will show a further increase, perhaps to 10 percent, a symbolic milestone with heavy political significance.

The president has been scheduled to be in California on that highly charged date, but administration officials said yesterday that the schedule "is now in a state of flux."

With a jobs bill enacted before they go home to campaign, Republicans would have something with which to counter the Democratic finger pointing on the unemployment front.

The House recently passed a $1 billion emergency jobs program, backed by Democratic leaders, to create 200,000 temporary public works jobs. White House aides have said the president definitely would veto that one.

As for the jobs training bill, Hatch yesterday credited the White House with breaking it loose, by "being willing to work out and accept compromises as well as for insisting on good stewardship of the public dollar."

The go-ahead signal came late Wednesday, during a meeting of Reagan, Hatch, Sen. Dan Quayle (R-Ind.) and Reps. John N. Erlenborn (R-Ill.), Augustus F. Hawkins (D-Calif.) and James M. Jeffords (R-Vt.), Hatch said.

Yesterday, as House-Senate conferees went to work to get the bill into final form, Treasury Secretary Donald T. Regan read the president's statement urging passage.

The Senate version would require about $3.8 billion, compared with $5.4 billion in the House version. The final amount is still being worked out, an aide said.